36x-2=4/11x

Solution for 36x-2=4/11x equation:

36x-2=4/11x

We move all terms to the left:

36x-2-(4/11x)=0


Domain of the equation: 11x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

36x-(+4/11x)-2=0

We get rid of parentheses

36x-4/11x-2=0

We multiply all the terms by the denominator


36x*11x-2*11x-4=0

Wy multiply elements

396x^2-22x-4=0

a = 396; b = -22; c = -4;
Δ = b2-4ac
Δ = -222-4·396·(-4)
Δ = 6820
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:

$\sqrt{\Delta}=\sqrt{6820}=\sqrt{4*1705}=\sqrt{4}*\sqrt{1705}=2\sqrt{1705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{1705}}{2*396}=\frac{22-2\sqrt{1705}}{792}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{1705}}{2*396}=\frac{22+2\sqrt{1705}}{792}
$