5/2x+8=4x

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

5/2x+8=4x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2+16x+5=0

a = -8; b = 16; c = +5;
Δ = b2-4ac
Δ = 162-4·(-8)·5
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{26}}{2*-8}=\frac{-16-4\sqrt{26}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{26}}{2*-8}=\frac{-16+4\sqrt{26}}{-16}
$