4x(x-5)=48

Solution for 4x(x-5)=48 equation:

4x(x-5)=48

We move all terms to the left:

4x(x-5)-(48)=0

We multiply parentheses

4x^2-20x-48=0

a = 4; b = -20; c = -48;
Δ = b2-4ac
Δ = -202-4·4·(-48)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{73}}{2*4}=\frac{20-4\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{73}}{2*4}=\frac{20+4\sqrt{73}}{8}
$