(10+x)(6+x)=117

Solution for (10+x)(6+x)=117 equation:

(10+x)(6+x)=117

We move all terms to the left:

(10+x)(6+x)-(117)=0

We add all the numbers together, and all the variables

(x+10)(x+6)-117=0

We multiply parentheses ..

(+x^2+6x+10x+60)-117=0

We get rid of parentheses

x^2+6x+10x+60-117=0

We add all the numbers together, and all the variables

x^2+16x-57=0

a = 1; b = 16; c = -57;
Δ = b2-4ac
Δ = 162-4·1·(-57)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-22}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+22}{2*1}=\frac{6}{2}
=3
$