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X^2+18X-1092=0
a = 1; b = 18; c = -1092;
Δ = b2-4ac
Δ = 182-4·1·(-1092)
Δ = 4692
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4692}=\sqrt{4*1173}=\sqrt{4}*\sqrt{1173}=2\sqrt{1173}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{1173}}{2*1}=\frac{-18-2\sqrt{1173}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{1173}}{2*1}=\frac{-18+2\sqrt{1173}}{2} $
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