X^2+23y+3=180

Solution for X^2+23y+3=180 equation:

X^2+23X+3=180

We move all terms to the left:

X^2+23X+3-(180)=0

We add all the numbers together, and all the variables

X^2+23X-177=0

a = 1; b = 23; c = -177;
Δ = b2-4ac
Δ = 232-4·1·(-177)
Δ = 1237
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{1237}}{2*1}=\frac{-23-\sqrt{1237}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{1237}}{2*1}=\frac{-23+\sqrt{1237}}{2}
$