5(4x-1)(6x-1)=0

Solution for 5(4x-1)(6x-1)=0 equation:

5(4x-1)(6x-1)=0

We multiply parentheses ..

5(+24x^2-4x-6x+1)=0

We multiply parentheses

120x^2-20x-30x+5=0

We add all the numbers together, and all the variables

120x^2-50x+5=0

a = 120; b = -50; c = +5;
Δ = b2-4ac
Δ = -502-4·120·5
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10}{2*120}=\frac{40}{240}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10}{2*120}=\frac{60}{240}
=1/4
$