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

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

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

We move all terms to the left:

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


Domain of the equation: 2x)+(x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2+2x^2+2x-92x+1=0

We add all the numbers together, and all the variables

4x^2-90x+1=0

a = 4; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·4·1
Δ = 8084
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:

$\sqrt{\Delta}=\sqrt{8084}=\sqrt{4*2021}=\sqrt{4}*\sqrt{2021}=2\sqrt{2021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2021}}{2*4}=\frac{90-2\sqrt{2021}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2021}}{2*4}=\frac{90+2\sqrt{2021}}{8}
$