X(x-13)+6x=18

Solution for X(x-13)+6x=18 equation:

X(X-13)+6X=18

We move all terms to the left:

X(X-13)+6X-(18)=0

We add all the numbers together, and all the variables

6X+X(X-13)-18=0

We multiply parentheses

X^2+6X-13X-18=0

We add all the numbers together, and all the variables

X^2-7X-18=0

a = 1; b = -7; c = -18;
Δ = b2-4ac
Δ = -72-4·1·(-18)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*1}=\frac{18}{2}
=9
$