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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


x*2x+x+x*2x+1-46=0

We add all the numbers together, and all the variables

x+x*2x+x*2x-45=0

Wy multiply elements

2x^2+2x^2+x-45=0

We add all the numbers together, and all the variables

4x^2+x-45=0

a = 4; b = 1; c = -45;
Δ = b2-4ac
Δ = 12-4·4·(-45)
Δ = 721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{721}}{2*4}=\frac{-1-\sqrt{721}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{721}}{2*4}=\frac{-1+\sqrt{721}}{8}
$