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

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

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

We move all terms to the left:

X-35+X-X-46+1/2X-(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-441=0

We multiply all the terms by the denominator


X*2X-441*2X+1=0

Wy multiply elements

2X^2-882X+1=0

a = 2; b = -882; c = +1;
Δ = b2-4ac
Δ = -8822-4·2·1
Δ = 777916
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:

$\sqrt{\Delta}=\sqrt{777916}=\sqrt{4*194479}=\sqrt{4}*\sqrt{194479}=2\sqrt{194479}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-882)-2\sqrt{194479}}{2*2}=\frac{882-2\sqrt{194479}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-882)+2\sqrt{194479}}{2*2}=\frac{882+2\sqrt{194479}}{4}
$