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^2-22x+60=0

a = 2; b = -22; c = +60;
Δ = b2-4ac
Δ = -222-4·2·60
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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