x+(x-35)+(x-45)+1/2x=180

Solution for x+(x-35)+(x-45)+1/2x=180 equation:

x+(x-35)+(x-45)+1/2x=180

We move all terms to the left:

x+(x-35)+(x-45)+1/2x-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x+x+x+1/2x-35-45-180=0

We multiply all the terms by the denominator


x*2x+x*2x+x*2x-35*2x-45*2x-180*2x+1=0

Wy multiply elements

2x^2+2x^2+2x^2-70x-90x-360x+1=0

We add all the numbers together, and all the variables

6x^2-520x+1=0

a = 6; b = -520; c = +1;
Δ = b2-4ac
Δ = -5202-4·6·1
Δ = 270376
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:

$\sqrt{\Delta}=\sqrt{270376}=\sqrt{4*67594}=\sqrt{4}*\sqrt{67594}=2\sqrt{67594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-520)-2\sqrt{67594}}{2*6}=\frac{520-2\sqrt{67594}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-520)+2\sqrt{67594}}{2*6}=\frac{520+2\sqrt{67594}}{12}
$