(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!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-120x+1=0

a = 4; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·4·1
Δ = 14384
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:

$\sqrt{\Delta}=\sqrt{14384}=\sqrt{16*899}=\sqrt{16}*\sqrt{899}=4\sqrt{899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{899}}{2*4}=\frac{120-4\sqrt{899}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{899}}{2*4}=\frac{120+4\sqrt{899}}{8}
$