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X^2-4X=100
We move all terms to the left:
X^2-4X-(100)=0
a = 1; b = -4; c = -100;
Δ = b2-4ac
Δ = -42-4·1·(-100)
Δ = 416
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{26}}{2*1}=\frac{4-4\sqrt{26}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{26}}{2*1}=\frac{4+4\sqrt{26}}{2} $
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