30/(2x-1)=2x

Solution for 30/(2x-1)=2x equation:

30/(2x-1)=2x

We move all terms to the left:

30/(2x-1)-(2x)=0


Domain of the equation: (2x-1)!=0

We move all terms containing x to the left, all other terms to the right

2x!=1

x!=1/2

x!=1/2

x∈R


We add all the numbers together, and all the variables

-2x+30/(2x-1)=0

We multiply all the terms by the denominator


-2x*(2x-1)+30=0

We multiply parentheses

-4x^2+2x+30=0

a = -4; b = 2; c = +30;
Δ = b2-4ac
Δ = 22-4·(-4)·30
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*-4}=\frac{20}{-8}
=-2+1/2
$