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x^2+38x-323=0
a = 1; b = 38; c = -323;
Δ = b2-4ac
Δ = 382-4·1·(-323)
Δ = 2736
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-12\sqrt{19}}{2*1}=\frac{-38-12\sqrt{19}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+12\sqrt{19}}{2*1}=\frac{-38+12\sqrt{19}}{2} $
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