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x^2+12x-231=0
a = 1; b = 12; c = -231;
Δ = b2-4ac
Δ = 122-4·1·(-231)
Δ = 1068
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1068}=\sqrt{4*267}=\sqrt{4}*\sqrt{267}=2\sqrt{267}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{267}}{2*1}=\frac{-12-2\sqrt{267}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{267}}{2*1}=\frac{-12+2\sqrt{267}}{2} $
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