48=4x(x+5)

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

48=4x(x+5)

We move all terms to the left:

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


We calculate terms in parentheses: -(4x(x+5)), so:

4x(x+5)

We multiply parentheses

4x^2+20x

Back to the equation:

-(4x^2+20x)


We get rid of 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}
$