x^2+4x+28=180

Solution for x^2+4x+28=180 equation:

x^2+4x+28=180

We move all terms to the left:

x^2+4x+28-(180)=0

We add all the numbers together, and all the variables

x^2+4x-152=0

a = 1; b = 4; c = -152;
Δ = b2-4ac
Δ = 42-4·1·(-152)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{39}}{2*1}=\frac{-4-4\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{39}}{2*1}=\frac{-4+4\sqrt{39}}{2}
$