2x=5/4x+8

Solution for 2x=5/4x+8 equation:

2x=5/4x+8

We move all terms to the left:

2x-(5/4x+8)=0


Domain of the equation: 4x+8)!=0

x∈R


We get rid of parentheses

2x-5/4x-8=0

We multiply all the terms by the denominator


2x*4x-8*4x-5=0

Wy multiply elements

8x^2-32x-5=0

a = 8; b = -32; c = -5;
Δ = b2-4ac
Δ = -322-4·8·(-5)
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{74}}{2*8}=\frac{32-4\sqrt{74}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{74}}{2*8}=\frac{32+4\sqrt{74}}{16}
$