x^2-2+4x+7=180

Solution for x^2-2+4x+7=180 equation:

x^2-2+4x+7=180

We move all terms to the left:

x^2-2+4x+7-(180)=0

We add all the numbers together, and all the variables

x^2+4x-175=0

a = 1; b = 4; c = -175;
Δ = b2-4ac
Δ = 42-4·1·(-175)
Δ = 716
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:

$\sqrt{\Delta}=\sqrt{716}=\sqrt{4*179}=\sqrt{4}*\sqrt{179}=2\sqrt{179}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{179}}{2*1}=\frac{-4-2\sqrt{179}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{179}}{2*1}=\frac{-4+2\sqrt{179}}{2}
$