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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x+x+x+1/2x-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}
$