1/x-2=5x/4x+3

Solution for 1/x-2=5x/4x+3 equation:

1/x-2=5x/4x+3

We move all terms to the left:

1/x-2-(5x/4x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

1/x-5x/4x-3-2=0

We calculate fractions


(-5x^2)/4x^2+4x/4x^2-3-2=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-5x^2)+4x-5*4x^2=0

Wy multiply elements

(-5x^2)-20x^2+4x=0

We get rid of parentheses

-5x^2-20x^2+4x=0

We add all the numbers together, and all the variables

-25x^2+4x=0

a = -25; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-25)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-25}=\frac{-8}{-50}
=4/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-25}=\frac{0}{-50}
=0
$