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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


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

We add all the numbers together, and all the variables

x+(x-35)+1/2x-406=0

We get rid of parentheses

x+x+1/2x-35-406=0

We multiply all the terms by the denominator


x*2x+x*2x-35*2x-406*2x+1=0

Wy multiply elements

2x^2+2x^2-70x-812x+1=0

We add all the numbers together, and all the variables

4x^2-882x+1=0

a = 4; b = -882; c = +1;
Δ = b2-4ac
Δ = -8822-4·4·1
Δ = 777908
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:

$\sqrt{\Delta}=\sqrt{777908}=\sqrt{4*194477}=\sqrt{4}*\sqrt{194477}=2\sqrt{194477}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-882)-2\sqrt{194477}}{2*4}=\frac{882-2\sqrt{194477}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-882)+2\sqrt{194477}}{2*4}=\frac{882+2\sqrt{194477}}{8}
$