(5x+10)(6x-18)=0

Solution for (5x+10)(6x-18)=0 equation:

(5x+10)(6x-18)=0

We multiply parentheses ..

(+30x^2-90x+60x-180)=0

We get rid of parentheses

30x^2-90x+60x-180=0

We add all the numbers together, and all the variables

30x^2-30x-180=0

a = 30; b = -30; c = -180;
Δ = b2-4ac
Δ = -302-4·30·(-180)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-150}{2*30}=\frac{-120}{60}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+150}{2*30}=\frac{180}{60}
=3
$