36=3x-11/2x

Solution for 36=3x-11/2x equation:

36=3x-11/2x

We move all terms to the left:

36-(3x-11/2x)=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-11/2x)+36=0

We get rid of parentheses

-3x+11/2x+36=0

We multiply all the terms by the denominator


-3x*2x+36*2x+11=0

Wy multiply elements

-6x^2+72x+11=0

a = -6; b = 72; c = +11;
Δ = b2-4ac
Δ = 722-4·(-6)·11
Δ = 5448
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:

$\sqrt{\Delta}=\sqrt{5448}=\sqrt{4*1362}=\sqrt{4}*\sqrt{1362}=2\sqrt{1362}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1362}}{2*-6}=\frac{-72-2\sqrt{1362}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1362}}{2*-6}=\frac{-72+2\sqrt{1362}}{-12}
$