(5x-3)(6x-12)=0

Solution for (5x-3)(6x-12)=0 equation:

(5x-3)(6x-12)=0

We multiply parentheses ..

(+30x^2-60x-18x+36)=0

We get rid of parentheses

30x^2-60x-18x+36=0

We add all the numbers together, and all the variables

30x^2-78x+36=0

a = 30; b = -78; c = +36;
Δ = b2-4ac
Δ = -782-4·30·36
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-42}{2*30}=\frac{36}{60}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+42}{2*30}=\frac{120}{60}
=2
$