x-18+x+(1/2)x=180

Solution for x-18+x+(1/2)x=180 equation:

x-18+x+(1/2)x=180

We move all terms to the left:

x-18+x+(1/2)x-(180)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+x+(+1/2)x-18-180=0

We add all the numbers together, and all the variables

2x+(+1/2)x-198=0

We multiply parentheses

x^2+2x-198=0

a = 1; b = 2; c = -198;
Δ = b2-4ac
Δ = 22-4·1·(-198)
Δ = 796
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{199}}{2*1}=\frac{-2-2\sqrt{199}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{199}}{2*1}=\frac{-2+2\sqrt{199}}{2}
$