(9+x)(6+x)=130

Solution for (9+x)(6+x)=130 equation:

(9+x)(6+x)=130

We move all terms to the left:

(9+x)(6+x)-(130)=0

We add all the numbers together, and all the variables

(x+9)(x+6)-130=0

We multiply parentheses ..

(+x^2+6x+9x+54)-130=0

We get rid of parentheses

x^2+6x+9x+54-130=0

We add all the numbers together, and all the variables

x^2+15x-76=0

a = 1; b = 15; c = -76;
Δ = b2-4ac
Δ = 152-4·1·(-76)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-23}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+23}{2*1}=\frac{8}{2}
=4
$