(6x-1)(5x-1)=8

Solution for (6x-1)(5x-1)=8 equation:

(6x-1)(5x-1)=8

We move all terms to the left:

(6x-1)(5x-1)-(8)=0

We multiply parentheses ..

(+30x^2-6x-5x+1)-8=0

We get rid of parentheses

30x^2-6x-5x+1-8=0

We add all the numbers together, and all the variables

30x^2-11x-7=0

a = 30; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·30·(-7)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-31}{2*30}=\frac{-20}{60}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*30}=\frac{42}{60}
=7/10
$