(10+x)*x=80+x

Solution for (10+x)*x=80+x equation:

(10+x)*x=80+x

We move all terms to the left:

(10+x)*x-(80+x)=0

We add all the numbers together, and all the variables

(x+10)*x-(x+80)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+9x-80=0

a = 1; b = 9; c = -80;
Δ = b2-4ac
Δ = 92-4·1·(-80)
Δ = 401
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{-(9)-\sqrt{401}}{2*1}=\frac{-9-\sqrt{401}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{401}}{2*1}=\frac{-9+\sqrt{401}}{2}
$