(10+x)(8+x)=224

Solution for (10+x)(8+x)=224 equation:

(10+x)(8+x)=224

We move all terms to the left:

(10+x)(8+x)-(224)=0

We add all the numbers together, and all the variables

(x+10)(x+8)-224=0

We multiply parentheses ..

(+x^2+8x+10x+80)-224=0

We get rid of parentheses

x^2+8x+10x+80-224=0

We add all the numbers together, and all the variables

x^2+18x-144=0

a = 1; b = 18; c = -144;
Δ = b2-4ac
Δ = 182-4·1·(-144)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*1}=\frac{12}{2}
=6
$