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)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-81=0

We multiply all the terms by the denominator


3x*2x-81*2x+1=0

Wy multiply elements

6x^2-162x+1=0

a = 6; b = -162; c = +1;
Δ = b2-4ac
Δ = -1622-4·6·1
Δ = 26220
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:

$\sqrt{\Delta}=\sqrt{26220}=\sqrt{4*6555}=\sqrt{4}*\sqrt{6555}=2\sqrt{6555}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-2\sqrt{6555}}{2*6}=\frac{162-2\sqrt{6555}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+2\sqrt{6555}}{2*6}=\frac{162+2\sqrt{6555}}{12}
$