X^2-1+3x+9=180

Solution for X^2-1+3x+9=180 equation:

X^2-1+3X+9=180

We move all terms to the left:

X^2-1+3X+9-(180)=0

We add all the numbers together, and all the variables

X^2+3X-172=0

a = 1; b = 3; c = -172;
Δ = b2-4ac
Δ = 32-4·1·(-172)
Δ = 697
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{-(3)-\sqrt{697}}{2*1}=\frac{-3-\sqrt{697}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{697}}{2*1}=\frac{-3+\sqrt{697}}{2}
$