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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-360!=0

We move all terms containing x to the left, all other terms to the right

2x!=360

x!=360/2

x!=180

x∈R


We multiply all the terms by the denominator


x*2x+x+x*2x-360-360-46-35)+1=0

We add all the numbers together, and all the variables

x+x*2x+x*2x=0

Wy multiply elements

2x^2+2x^2+x=0

We add all the numbers together, and all the variables

4x^2+x=0

a = 4; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·4·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*4}=\frac{-2}{8}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*4}=\frac{0}{8}
=0
$