5/x+1/2=25/4x

Solution for 5/x+1/2=25/4x equation:

5/x+1/2=25/4x

We move all terms to the left:

5/x+1/2-(25/4x)=0


Domain of the equation: 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

5/x-(+25/4x)+1/2=0

We get rid of parentheses

5/x-25/4x+1/2=0

We calculate fractions


16x^2/16x^2+80x/16x^2+(-100x)/16x^2=0

Fractions to decimals

80x/16x^2+(-100x)/16x^2+1=0

We multiply all the terms by the denominator


80x+(-100x)+1*16x^2=0

Wy multiply elements

16x^2+80x+(-100x)=0

We get rid of parentheses

16x^2+80x-100x=0

We add all the numbers together, and all the variables

16x^2-20x=0

a = 16; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·16·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*16}=\frac{40}{32}
=1+1/4
$