52=4x(x+1)

Solution for 52=4x(x+1) equation:

52=4x(x+1)

We move all terms to the left:

52-(4x(x+1))=0


We calculate terms in parentheses: -(4x(x+1)), so:

4x(x+1)

We multiply parentheses

4x^2+4x

Back to the equation:

-(4x^2+4x)


We get rid of parentheses

-4x^2-4x+52=0

a = -4; b = -4; c = +52;
Δ = b2-4ac
Δ = -42-4·(-4)·52
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{53}}{2*-4}=\frac{4-4\sqrt{53}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{53}}{2*-4}=\frac{4+4\sqrt{53}}{-8}
$