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

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

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

We move all terms to the left:

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


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

-(2X-1/2X-81)+360=0

We get rid of parentheses

-2X+1/2X+81+360=0

We multiply all the terms by the denominator


-2X*2X+81*2X+360*2X+1=0

Wy multiply elements

-4X^2+162X+720X+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 = 777940
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:

$\sqrt{\Delta}=\sqrt{777940}=\sqrt{4*194485}=\sqrt{4}*\sqrt{194485}=2\sqrt{194485}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(882)-2\sqrt{194485}}{2*-4}=\frac{-882-2\sqrt{194485}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(882)+2\sqrt{194485}}{2*-4}=\frac{-882+2\sqrt{194485}}{-8}
$