4x^2+52x=4

Solution for 4x^2+52x=4 equation:

4x^2+52x=4

We move all terms to the left:

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

a = 4; b = 52; c = -4;
Δ = b2-4ac
Δ = 522-4·4·(-4)
Δ = 2768
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:

$\sqrt{\Delta}=\sqrt{2768}=\sqrt{16*173}=\sqrt{16}*\sqrt{173}=4\sqrt{173}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{173}}{2*4}=\frac{-52-4\sqrt{173}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{173}}{2*4}=\frac{-52+4\sqrt{173}}{8}
$