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X^2-14X-155=0
a = 1; b = -14; c = -155;
Δ = b2-4ac
Δ = -142-4·1·(-155)
Δ = 816
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{51}}{2*1}=\frac{14-4\sqrt{51}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{51}}{2*1}=\frac{14+4\sqrt{51}}{2} $
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