structural:summarization, linguistic:translation
Algebra

Brahmagupta gave the solution of the general linear equation in chapter eighteen of Brahmasphuṭasiddhānta,

The difference between rupas, when inverted and divided by the difference of the of the, is the unknown in the equation. The rupas are below that from which the square and the unknown are to be subtracted.

which is a solution for the equation bx + c = dx + e where rupas refers to the constants c and e. The solution given is equivalent to x = e − c / b − d.

He further gave two equivalent solutions to the general quadratic equation

18.44. Diminish by the middle the square-root of the rupas multiplied by four times the square and increased by the square of the middle; divide the remainder by twice the square. the middle. 18.45. Whatever is the square-root of the rupas multiplied by the square increased by the square of half the unknown, diminished that by half the unknown divide by its square. the unknown.

which are, respectively, solutions for the equation ax + bx = c equivalent to,

and

He went on to solve systems of simultaneous indeterminate equations stating that the desired variable must first be isolated, and then the equation must be divided by the desired variable's coefficient. In particular, he recommended using "the pulverizer" to solve equations with multiple unknowns.

18.51. Subtract the colors different from the first color. divided by the first is the measure of the first. two by two considered similar divisors, repeatedly. If there are many, the pulverizer.

Like the algebra of Diophantus, the algebra of Brahmagupta was syncopated. Addition was indicated by placing the numbers side by side, subtraction by placing a dot over the subtrahend, and division by placing the divisor below the dividend, similar to our notation but without the bar. Multiplication, evolution, and unknown quantities were represented by abbreviations of appropriate terms. The extent of Greek influence on this syncopation, if any, is not known and it is possible that both Greek and Indian syncopation may be derived from a common Babylonian source.