2(x-5)(x-7)=0

Solution for 2(x-5)(x-7)=0 equation:

2(x-5)(x-7)=0

We multiply parentheses ..

2(+x^2-7x-5x+35)=0

We multiply parentheses

2x^2-14x-10x+70=0

We add all the numbers together, and all the variables

2x^2-24x+70=0

a = 2; b = -24; c = +70;
Δ = b2-4ac
Δ = -242-4·2·70
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4}{2*2}=\frac{20}{4}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4}{2*2}=\frac{28}{4}
=7
$