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X^2+6X=106
We move all terms to the left:
X^2+6X-(106)=0
a = 1; b = 6; c = -106;
Δ = b2-4ac
Δ = 62-4·1·(-106)
Δ = 460
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{115}}{2*1}=\frac{-6-2\sqrt{115}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{115}}{2*1}=\frac{-6+2\sqrt{115}}{2} $
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