x^2-50+5x=180

Solution for x^2-50+5x=180 equation:

x^2-50+5x=180

We move all terms to the left:

x^2-50+5x-(180)=0

We add all the numbers together, and all the variables

x^2+5x-230=0

a = 1; b = 5; c = -230;
Δ = b2-4ac
Δ = 52-4·1·(-230)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{105}}{2*1}=\frac{-5-3\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{105}}{2*1}=\frac{-5+3\sqrt{105}}{2}
$