2x-5/4x=13

Solution for 2x-5/4x=13 equation:

2x-5/4x=13

We move all terms to the left:

2x-5/4x-(13)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-13*4x-5=0

Wy multiply elements

8x^2-52x-5=0

a = 8; b = -52; c = -5;
Δ = b2-4ac
Δ = -522-4·8·(-5)
Δ = 2864
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:

$\sqrt{\Delta}=\sqrt{2864}=\sqrt{16*179}=\sqrt{16}*\sqrt{179}=4\sqrt{179}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{179}}{2*8}=\frac{52-4\sqrt{179}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{179}}{2*8}=\frac{52+4\sqrt{179}}{16}
$