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x(x-15)+x+x-2=120
We move all terms to the left:
x(x-15)+x+x-2-(120)=0
We add all the numbers together, and all the variables
2x+x(x-15)-122=0
We multiply parentheses
x^2+2x-15x-122=0
We add all the numbers together, and all the variables
x^2-13x-122=0
a = 1; b = -13; c = -122;
Δ = b2-4ac
Δ = -132-4·1·(-122)
Δ = 657
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{73}}{2*1}=\frac{13-3\sqrt{73}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{73}}{2*1}=\frac{13+3\sqrt{73}}{2} $
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