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

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

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

We multiply parentheses ..

(+6x^2-3x-30x+15)=0

We get rid of parentheses

6x^2-3x-30x+15=0

We add all the numbers together, and all the variables

6x^2-33x+15=0

a = 6; b = -33; c = +15;
Δ = b2-4ac
Δ = -332-4·6·15
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-27}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+27}{2*6}=\frac{60}{12}
=5
$