(x-6)(x-10)=0

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

(x-6)(x-10)=0

We multiply parentheses ..

(+x^2-10x-6x+60)=0

We get rid of parentheses

x^2-10x-6x+60=0

We add all the numbers together, and all the variables

x^2-16x+60=0

a = 1; b = -16; c = +60;
Δ = b2-4ac
Δ = -162-4·1·60
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{-(-16)-4}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4}{2*1}=\frac{20}{2}
=10
$