8/2x+5=4x+5

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

8/2x+5=4x+5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2-10x+10x+8=0

We add all the numbers together, and all the variables

-8x^2+8=0

a = -8; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-8)·8
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*-8}=\frac{-16}{-16}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*-8}=\frac{16}{-16}
=-1
$