13x-2/2x+1=4Q

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

13x-2/2x+1=4

We move all terms to the left:

13x-2/2x+1-(4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

13x-2/2x-3=0

We multiply all the terms by the denominator


13x*2x-3*2x-2=0

Wy multiply elements

26x^2-6x-2=0

a = 26; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·26·(-2)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{61}}{2*26}=\frac{6-2\sqrt{61}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{61}}{2*26}=\frac{6+2\sqrt{61}}{52}
$