(5x+10)(9x-6)=0

Solution for (5x+10)(9x-6)=0 equation:

(5x+10)(9x-6)=0

We multiply parentheses ..

(+45x^2-30x+90x-60)=0

We get rid of parentheses

45x^2-30x+90x-60=0

We add all the numbers together, and all the variables

45x^2+60x-60=0

a = 45; b = 60; c = -60;
Δ = b2-4ac
Δ = 602-4·45·(-60)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-120}{2*45}=\frac{-180}{90}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+120}{2*45}=\frac{60}{90}
=2/3
$