x+x(1/2x+10)=180

Solution for x+x(1/2x+10)=180 equation:

x+x(1/2x+10)=180

We move all terms to the left:

x+x(1/2x+10)-(180)=0


Domain of the equation: 2x+10)!=0

x∈R


We multiply parentheses

x^2+x+10x-180=0

We add all the numbers together, and all the variables

x^2+11x-180=0

a = 1; b = 11; c = -180;
Δ = b2-4ac
Δ = 112-4·1·(-180)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-29}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+29}{2*1}=\frac{18}{2}
=9
$