9q^2-3q=-8q^2-5q+15

Solution for 9q^2-3q=-8q^2-5q+15 equation:

9q^2-3q=-8q^2-5q+15

We move all terms to the left:

9q^2-3q-(-8q^2-5q+15)=0

We get rid of parentheses

9q^2+8q^2+5q-3q-15=0

We add all the numbers together, and all the variables

17q^2+2q-15=0

a = 17; b = 2; c = -15;
Δ = b2-4ac
Δ = 22-4·17·(-15)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-32}{2*17}=\frac{-34}{34}
=-1
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+32}{2*17}=\frac{30}{34}
=15/17
$