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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2+2x^2+2x^2-70x-92x-720x+1=0

We add all the numbers together, and all the variables

6x^2-882x+1=0

a = 6; b = -882; c = +1;
Δ = b2-4ac
Δ = -8822-4·6·1
Δ = 777900
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:

$\sqrt{\Delta}=\sqrt{777900}=\sqrt{100*7779}=\sqrt{100}*\sqrt{7779}=10\sqrt{7779}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-882)-10\sqrt{7779}}{2*6}=\frac{882-10\sqrt{7779}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-882)+10\sqrt{7779}}{2*6}=\frac{882+10\sqrt{7779}}{12}
$