x2-23x+55=180

Solution for x2-23x+55=180 equation:

x2-23x+55=180

We move all terms to the left:

x2-23x+55-(180)=0

We add all the numbers together, and all the variables

x^2-23x-125=0

a = 1; b = -23; c = -125;
Δ = b2-4ac
Δ = -232-4·1·(-125)
Δ = 1029
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:

$\sqrt{\Delta}=\sqrt{1029}=\sqrt{49*21}=\sqrt{49}*\sqrt{21}=7\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-7\sqrt{21}}{2*1}=\frac{23-7\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7\sqrt{21}}{2*1}=\frac{23+7\sqrt{21}}{2}
$