4x^2+152x+552=0

Solution for 4x^2+152x+552=0 equation:

4x^2+152x+552=0

a = 4; b = 152; c = +552;
Δ = b2-4ac
Δ = 1522-4·4·552
Δ = 14272
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:

$\sqrt{\Delta}=\sqrt{14272}=\sqrt{64*223}=\sqrt{64}*\sqrt{223}=8\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(152)-8\sqrt{223}}{2*4}=\frac{-152-8\sqrt{223}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(152)+8\sqrt{223}}{2*4}=\frac{-152+8\sqrt{223}}{8}
$