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X^2-5X=102
We move all terms to the left:
X^2-5X-(102)=0
a = 1; b = -5; c = -102;
Δ = b2-4ac
Δ = -52-4·1·(-102)
Δ = 433
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{433}}{2*1}=\frac{5-\sqrt{433}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{433}}{2*1}=\frac{5+\sqrt{433}}{2} $
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