(3x-5)(6x-1)=0

Solution for (3x-5)(6x-1)=0 equation:

(3x-5)(6x-1)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

18x^2-33x+5=0

a = 18; b = -33; c = +5;
Δ = b2-4ac
Δ = -332-4·18·5
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*18}=\frac{6}{36}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+27}{2*18}=\frac{60}{36}
=1+2/3
$