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

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

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

We move all terms to the left:

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


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

X+X+X+1/2X-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}
$