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

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

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

We multiply parentheses ..

(+3x^2-5x-18x+30)=0

We get rid of parentheses

3x^2-5x-18x+30=0

We add all the numbers together, and all the variables

3x^2-23x+30=0

a = 3; b = -23; c = +30;
Δ = b2-4ac
Δ = -232-4·3·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-13}{2*3}=\frac{10}{6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+13}{2*3}=\frac{36}{6}
=6
$