X+(x-46)+1/2x+(x-35)=180

Solution for X+(x-46)+1/2x+(x-35)=180 equation:

X+(X-46)+1/2X+(X-35)=180

We move all terms to the left:

X+(X-46)+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+X+1/2X+X-46-35-180=0

We multiply all the terms by the denominator


X*2X+X*2X+X*2X-46*2X-35*2X-180*2X+1=0

Wy multiply elements

2X^2+2X^2+2X^2-92X-70X-360X+1=0

We add all the numbers together, and all the variables

6X^2-522X+1=0

a = 6; b = -522; c = +1;
Δ = b2-4ac
Δ = -5222-4·6·1
Δ = 272460
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:

$\sqrt{\Delta}=\sqrt{272460}=\sqrt{4*68115}=\sqrt{4}*\sqrt{68115}=2\sqrt{68115}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-522)-2\sqrt{68115}}{2*6}=\frac{522-2\sqrt{68115}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-522)+2\sqrt{68115}}{2*6}=\frac{522+2\sqrt{68115}}{12}
$