(x-35)+(x-25)+(1/2x-10)=180

Solution for (x-35)+(x-25)+(1/2x-10)=180 equation:

(x-35)+(x-25)+(1/2x-10)=180

We move all terms to the left:

(x-35)+(x-25)+(1/2x-10)-(180)=0


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

x∈R


We get rid of parentheses

x+x+1/2x-35-25-10-180=0

We multiply all the terms by the denominator


x*2x+x*2x-35*2x-25*2x-10*2x-180*2x+1=0

Wy multiply elements

2x^2+2x^2-70x-50x-20x-360x+1=0

We add all the numbers together, and all the variables

4x^2-500x+1=0

a = 4; b = -500; c = +1;
Δ = b2-4ac
Δ = -5002-4·4·1
Δ = 249984
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:

$\sqrt{\Delta}=\sqrt{249984}=\sqrt{576*434}=\sqrt{576}*\sqrt{434}=24\sqrt{434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-24\sqrt{434}}{2*4}=\frac{500-24\sqrt{434}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+24\sqrt{434}}{2*4}=\frac{500+24\sqrt{434}}{8}
$