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x^2+15x-152=0
a = 1; b = 15; c = -152;
Δ = b2-4ac
Δ = 152-4·1·(-152)
Δ = 833
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-7\sqrt{17}}{2*1}=\frac{-15-7\sqrt{17}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+7\sqrt{17}}{2*1}=\frac{-15+7\sqrt{17}}{2} $
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