2x+10=4/2x-1

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

2x+10=4/2x-1

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+2x+20x-4=0

We add all the numbers together, and all the variables

4x^2+22x-4=0

a = 4; b = 22; c = -4;
Δ = b2-4ac
Δ = 222-4·4·(-4)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{137}}{2*4}=\frac{-22-2\sqrt{137}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{137}}{2*4}=\frac{-22+2\sqrt{137}}{8}
$