(2x-10)(3x-12)=0

Solution for (2x-10)(3x-12)=0 equation:

(2x-10)(3x-12)=0

We multiply parentheses ..

(+6x^2-24x-30x+120)=0

We get rid of parentheses

6x^2-24x-30x+120=0

We add all the numbers together, and all the variables

6x^2-54x+120=0

a = 6; b = -54; c = +120;
Δ = b2-4ac
Δ = -542-4·6·120
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6}{2*6}=\frac{48}{12}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6}{2*6}=\frac{60}{12}
=5
$