5/4x=6/5x+2

Solution for 5/4x=6/5x+2 equation:

5/4x=6/5x+2

We move all terms to the left:

5/4x-(6/5x+2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

5/4x-6/5x-2=0

We calculate fractions


25x/20x^2+(-24x)/20x^2-2=0

We multiply all the terms by the denominator


25x+(-24x)-2*20x^2=0

Wy multiply elements

-40x^2+25x+(-24x)=0

We get rid of parentheses

-40x^2+25x-24x=0

We add all the numbers together, and all the variables

-40x^2+x=0

a = -40; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-40)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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