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140=x^2+7x+18
We move all terms to the left:
140-(x^2+7x+18)=0
We get rid of parentheses
-x^2-7x-18+140=0
We add all the numbers together, and all the variables
-1x^2-7x+122=0
a = -1; b = -7; c = +122;
Δ = b2-4ac
Δ = -72-4·(-1)·122
Δ = 537
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{-(-7)-\sqrt{537}}{2*-1}=\frac{7-\sqrt{537}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{537}}{2*-1}=\frac{7+\sqrt{537}}{-2} $
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