X+(x-35)+1/2x+(x+46)=360

Solution for X+(x-35)+1/2x+(x+46)=360 equation:

X+(X-35)+1/2X+(X+46)=360

We move all terms to the left:

X+(X-35)+1/2X+(X+46)-(360)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

X+X+1/2X+X-35+46-360=0

We multiply all the terms by the denominator


X*2X+X*2X+X*2X-35*2X+46*2X-360*2X+1=0

Wy multiply elements

2X^2+2X^2+2X^2-70X+92X-720X+1=0

We add all the numbers together, and all the variables

6X^2-698X+1=0

a = 6; b = -698; c = +1;
Δ = b2-4ac
Δ = -6982-4·6·1
Δ = 487180
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:

$\sqrt{\Delta}=\sqrt{487180}=\sqrt{4*121795}=\sqrt{4}*\sqrt{121795}=2\sqrt{121795}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-698)-2\sqrt{121795}}{2*6}=\frac{698-2\sqrt{121795}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-698)+2\sqrt{121795}}{2*6}=\frac{698+2\sqrt{121795}}{12}
$