(10+x)(8+x)=440

Solution for (10+x)(8+x)=440 equation:

(10+x)(8+x)=440

We move all terms to the left:

(10+x)(8+x)-(440)=0

We add all the numbers together, and all the variables

(x+10)(x+8)-440=0

We multiply parentheses ..

(+x^2+8x+10x+80)-440=0

We get rid of parentheses

x^2+8x+10x+80-440=0

We add all the numbers together, and all the variables

x^2+18x-360=0

a = 1; b = 18; c = -360;
Δ = b2-4ac
Δ = 182-4·1·(-360)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-42}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+42}{2*1}=\frac{24}{2}
=12
$