2x=10/4x-1

Solution for 2x=10/4x-1 equation:

2x=10/4x-1

We move all terms to the left:

2x-(10/4x-1)=0


Domain of the equation: 4x-1)!=0

x∈R


We get rid of parentheses

2x-10/4x+1=0

We multiply all the terms by the denominator


2x*4x+1*4x-10=0

Wy multiply elements

8x^2+4x-10=0

a = 8; b = 4; c = -10;
Δ = b2-4ac
Δ = 42-4·8·(-10)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{21}}{2*8}=\frac{-4-4\sqrt{21}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{21}}{2*8}=\frac{-4+4\sqrt{21}}{16}
$