180-34x+x^2=0

Solution for 180-34x+x^2=0 equation:

180-34x+x^2=0

a = 1; b = -34; c = +180;
Δ = b2-4ac
Δ = -342-4·1·180
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{109}}{2*1}=\frac{34-2\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{109}}{2*1}=\frac{34+2\sqrt{109}}{2}
$