13x-8/4x+1=2

Solution for 13x-8/4x+1=2 equation:

13x-8/4x+1=2

We move all terms to the left:

13x-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

13x-8/4x-1=0

We multiply all the terms by the denominator


13x*4x-1*4x-8=0

Wy multiply elements

52x^2-4x-8=0

a = 52; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·52·(-8)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{105}}{2*52}=\frac{4-4\sqrt{105}}{104}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{105}}{2*52}=\frac{4+4\sqrt{105}}{104}
$