23x-8/4x+1=2

Solution for 23x-8/4x+1=2 equation:

23x-8/4x+1=2

We move all terms to the left:

23x-8/4x+1-(2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

23x-8/4x-1=0

We multiply all the terms by the denominator


23x*4x-1*4x-8=0

Wy multiply elements

92x^2-4x-8=0

a = 92; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·92·(-8)
Δ = 2960
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:

$\sqrt{\Delta}=\sqrt{2960}=\sqrt{16*185}=\sqrt{16}*\sqrt{185}=4\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{185}}{2*92}=\frac{4-4\sqrt{185}}{184}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{185}}{2*92}=\frac{4+4\sqrt{185}}{184}
$