(x-10)(x-7)=0

Solution for (x-10)(x-7)=0 equation:

(x-10)(x-7)=0

We multiply parentheses ..

(+x^2-7x-10x+70)=0

We get rid of parentheses

x^2-7x-10x+70=0

We add all the numbers together, and all the variables

x^2-17x+70=0

a = 1; b = -17; c = +70;
Δ = b2-4ac
Δ = -172-4·1·70
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3}{2*1}=\frac{14}{2}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3}{2*1}=\frac{20}{2}
=10
$