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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-290x+1=0

a = 4; b = -290; c = +1;
Δ = b2-4ac
Δ = -2902-4·4·1
Δ = 84084
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:

$\sqrt{\Delta}=\sqrt{84084}=\sqrt{196*429}=\sqrt{196}*\sqrt{429}=14\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-290)-14\sqrt{429}}{2*4}=\frac{290-14\sqrt{429}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-290)+14\sqrt{429}}{2*4}=\frac{290+14\sqrt{429}}{8}
$