4x(3x-5)=52

Solution for 4x(3x-5)=52 equation:

4x(3x-5)=52

We move all terms to the left:

4x(3x-5)-(52)=0

We multiply parentheses

12x^2-20x-52=0

a = 12; b = -20; c = -52;
Δ = b2-4ac
Δ = -202-4·12·(-52)
Δ = 2896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2896}=\sqrt{16*181}=\sqrt{16}*\sqrt{181}=4\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{181}}{2*12}=\frac{20-4\sqrt{181}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{181}}{2*12}=\frac{20+4\sqrt{181}}{24}
$