(x-34)+(2x-118)+(1/2x+17)=180

Solution for (x-34)+(2x-118)+(1/2x+17)=180 equation:

(x-34)+(2x-118)+(1/2x+17)=180

We move all terms to the left:

(x-34)+(2x-118)+(1/2x+17)-(180)=0


Domain of the equation: 2x+17)!=0

x∈R


We get rid of parentheses

x+2x+1/2x-34-118+17-180=0

We multiply all the terms by the denominator


x*2x+2x*2x-34*2x-118*2x+17*2x-180*2x+1=0

Wy multiply elements

2x^2+4x^2-68x-236x+34x-360x+1=0

We add all the numbers together, and all the variables

6x^2-630x+1=0

a = 6; b = -630; c = +1;
Δ = b2-4ac
Δ = -6302-4·6·1
Δ = 396876
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:

$\sqrt{\Delta}=\sqrt{396876}=\sqrt{4*99219}=\sqrt{4}*\sqrt{99219}=2\sqrt{99219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99219}}{2*6}=\frac{630-2\sqrt{99219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99219}}{2*6}=\frac{630+2\sqrt{99219}}{12}
$