2x+5/4x=12

Solution for 2x+5/4x=12 equation:

2x+5/4x=12

We move all terms to the left:

2x+5/4x-(12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-12*4x+5=0

Wy multiply elements

8x^2-48x+5=0

a = 8; b = -48; c = +5;
Δ = b2-4ac
Δ = -482-4·8·5
Δ = 2144
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:

$\sqrt{\Delta}=\sqrt{2144}=\sqrt{16*134}=\sqrt{16}*\sqrt{134}=4\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{134}}{2*8}=\frac{48-4\sqrt{134}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{134}}{2*8}=\frac{48+4\sqrt{134}}{16}
$