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x^2+18x-72=90
We move all terms to the left:
x^2+18x-72-(90)=0
We add all the numbers together, and all the variables
x^2+18x-162=0
a = 1; b = 18; c = -162;
Δ = b2-4ac
Δ = 182-4·1·(-162)
Δ = 972
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{3}}{2*1}=\frac{-18-18\sqrt{3}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{3}}{2*1}=\frac{-18+18\sqrt{3}}{2} $
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