360=81+x+x+x+1/2x

Solution for 360=81+x+x+x+1/2x equation:

360=81+x+x+x+1/2x

We move all terms to the left:

360-(81+x+x+x+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

-(3x+1/2x+81)+360=0

We get rid of parentheses

-3x-1/2x-81+360=0

We multiply all the terms by the denominator


-3x*2x-81*2x+360*2x-1=0

Wy multiply elements

-6x^2-162x+720x-1=0

We add all the numbers together, and all the variables

-6x^2+558x-1=0

a = -6; b = 558; c = -1;
Δ = b2-4ac
Δ = 5582-4·(-6)·(-1)
Δ = 311340
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:

$\sqrt{\Delta}=\sqrt{311340}=\sqrt{4*77835}=\sqrt{4}*\sqrt{77835}=2\sqrt{77835}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(558)-2\sqrt{77835}}{2*-6}=\frac{-558-2\sqrt{77835}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(558)+2\sqrt{77835}}{2*-6}=\frac{-558+2\sqrt{77835}}{-12}
$