(X+13)y=9

Solution for (X+13)y=9 equation:

(X+13)X=9

We move all terms to the left:

(X+13)X-(9)=0

We multiply parentheses

X^2+13X-9=0

a = 1; b = 13; c = -9;
Δ = b2-4ac
Δ = 132-4·1·(-9)
Δ = 205
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{205}}{2*1}=\frac{-13-\sqrt{205}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{205}}{2*1}=\frac{-13+\sqrt{205}}{2}
$