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

Solution for 360=1/2x+3x+-81 equation:

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

We move all terms to the left:

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


Domain of the equation: 2x+3x+-81)!=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+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}
$