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X^2+32X+180=0
a = 1; b = 32; c = +180;
Δ = b2-4ac
Δ = 322-4·1·180
Δ = 304
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{19}}{2*1}=\frac{-32-4\sqrt{19}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{19}}{2*1}=\frac{-32+4\sqrt{19}}{2} $
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