4/2x+5=5/4x

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

4/2x+5=5/4x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


16x/8x^2+(-10x)/8x^2+5=0

We multiply all the terms by the denominator


16x+(-10x)+5*8x^2=0

Wy multiply elements

40x^2+16x+(-10x)=0

We get rid of parentheses

40x^2+16x-10x=0

We add all the numbers together, and all the variables

40x^2+6x=0

a = 40; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·40·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*40}=\frac{-12}{80}
=-3/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*40}=\frac{0}{80}
=0
$