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100=72+15x-x^2
We move all terms to the left:
100-(72+15x-x^2)=0
We get rid of parentheses
x^2-15x-72+100=0
We add all the numbers together, and all the variables
x^2-15x+28=0
a = 1; b = -15; c = +28;
Δ = b2-4ac
Δ = -152-4·1·28
Δ = 113
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{113}}{2*1}=\frac{15-\sqrt{113}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{113}}{2*1}=\frac{15+\sqrt{113}}{2} $
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