4x(x-39)=24

Solution for 4x(x-39)=24 equation:

4x(x-39)=24

We move all terms to the left:

4x(x-39)-(24)=0

We multiply parentheses

4x^2-156x-24=0

a = 4; b = -156; c = -24;
Δ = b2-4ac
Δ = -1562-4·4·(-24)
Δ = 24720
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:

$\sqrt{\Delta}=\sqrt{24720}=\sqrt{16*1545}=\sqrt{16}*\sqrt{1545}=4\sqrt{1545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-4\sqrt{1545}}{2*4}=\frac{156-4\sqrt{1545}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+4\sqrt{1545}}{2*4}=\frac{156+4\sqrt{1545}}{8}
$