x^2-50+5x+34=180

Solution for x^2-50+5x+34=180 equation:

x^2-50+5x+34=180

We move all terms to the left:

x^2-50+5x+34-(180)=0

We add all the numbers together, and all the variables

x^2+5x-196=0

a = 1; b = 5; c = -196;
Δ = b2-4ac
Δ = 52-4·1·(-196)
Δ = 809
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{-(5)-\sqrt{809}}{2*1}=\frac{-5-\sqrt{809}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{809}}{2*1}=\frac{-5+\sqrt{809}}{2}
$