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3x+39=x^2+18x+81
We move all terms to the left:
3x+39-(x^2+18x+81)=0
We get rid of parentheses
-x^2+3x-18x-81+39=0
We add all the numbers together, and all the variables
-1x^2-15x-42=0
a = -1; b = -15; c = -42;
Δ = b2-4ac
Δ = -152-4·(-1)·(-42)
Δ = 57
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{-(-15)-\sqrt{57}}{2*-1}=\frac{15-\sqrt{57}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{57}}{2*-1}=\frac{15+\sqrt{57}}{-2} $
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