(8+x)*(5+x)=140

Solution for (8+x)*(5+x)=140 equation:

(8+x)(5+x)=140

We move all terms to the left:

(8+x)(5+x)-(140)=0

We add all the numbers together, and all the variables

(x+8)(x+5)-140=0

We multiply parentheses ..

(+x^2+5x+8x+40)-140=0

We get rid of parentheses

x^2+5x+8x+40-140=0

We add all the numbers together, and all the variables

x^2+13x-100=0

a = 1; b = 13; c = -100;
Δ = b2-4ac
Δ = 132-4·1·(-100)
Δ = 569
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{569}}{2*1}=\frac{-13-\sqrt{569}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{569}}{2*1}=\frac{-13+\sqrt{569}}{2}
$