8x2-13x=9x2+3x

Solution for 8x2-13x=9x2+3x equation:

8x^2-13x=9x^2+3x

We move all terms to the left:

8x^2-13x-(9x^2+3x)=0

We get rid of parentheses

8x^2-9x^2-13x-3x=0

We add all the numbers together, and all the variables

-1x^2-16x=0

a = -1; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-1)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-1}=\frac{32}{-2}
=-16
$