X(x-15)+x+(x-2)=120

Solution for X(x-15)+x+(x-2)=120 equation:

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

X+X(X-15)+(X-2)-120=0

We multiply parentheses

X^2+X-15X+(X-2)-120=0

We get rid of parentheses

X^2+X-15X+X-2-120=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}
$