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X(X-15)+X+X-15=120
We move all terms to the left:
X(X-15)+X+X-15-(120)=0
We add all the numbers together, and all the variables
2X+X(X-15)-135=0
We multiply parentheses
X^2+2X-15X-135=0
We add all the numbers together, and all the variables
X^2-13X-135=0
a = 1; b = -13; c = -135;
Δ = b2-4ac
Δ = -132-4·1·(-135)
Δ = 709
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{-(-13)-\sqrt{709}}{2*1}=\frac{13-\sqrt{709}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{709}}{2*1}=\frac{13+\sqrt{709}}{2} $
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