X^2+2x+92=180

Solution for X^2+2x+92=180 equation:

X^2+2X+92=180

We move all terms to the left:

X^2+2X+92-(180)=0

We add all the numbers together, and all the variables

X^2+2X-88=0

a = 1; b = 2; c = -88;
Δ = b2-4ac
Δ = 22-4·1·(-88)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{89}}{2*1}=\frac{-2-2\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{89}}{2*1}=\frac{-2+2\sqrt{89}}{2}
$