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X^2+18X-37=7
We move all terms to the left:
X^2+18X-37-(7)=0
We add all the numbers together, and all the variables
X^2+18X-44=0
a = 1; b = 18; c = -44;
Δ = b2-4ac
Δ = 182-4·1·(-44)
Δ = 500
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10\sqrt{5}}{2*1}=\frac{-18-10\sqrt{5}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10\sqrt{5}}{2*1}=\frac{-18+10\sqrt{5}}{2} $
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