4x(x-23)=48

Solution for 4x(x-23)=48 equation:

4x(x-23)=48

We move all terms to the left:

4x(x-23)-(48)=0

We multiply parentheses

4x^2-92x-48=0

a = 4; b = -92; c = -48;
Δ = b2-4ac
Δ = -922-4·4·(-48)
Δ = 9232
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:

$\sqrt{\Delta}=\sqrt{9232}=\sqrt{16*577}=\sqrt{16}*\sqrt{577}=4\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-4\sqrt{577}}{2*4}=\frac{92-4\sqrt{577}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+4\sqrt{577}}{2*4}=\frac{92+4\sqrt{577}}{8}
$