2(x-5)(x+6)=0

Solution for 2(x-5)(x+6)=0 equation:

2(x-5)(x+6)=0

We multiply parentheses ..

2(+x^2+6x-5x-30)=0

We multiply parentheses

2x^2+12x-10x-60=0

We add all the numbers together, and all the variables

2x^2+2x-60=0

a = 2; b = 2; c = -60;
Δ = b2-4ac
Δ = 22-4·2·(-60)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*2}=\frac{20}{4}
=5
$