(3x^2-9x)-(5x^2+10x)=0

Solution for (3x^2-9x)-(5x^2+10x)=0 equation:

(3x^2-9x)-(5x^2+10x)=0

We get rid of parentheses

3x^2-5x^2-9x-10x=0

We add all the numbers together, and all the variables

-2x^2-19x=0

a = -2; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-2)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-2}=\frac{38}{-4}
=-9+1/2
$