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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

6x/2x^2+(-4x)/2x^2-7=0

We multiply all the terms by the denominator


6x+(-4x)-7*2x^2=0

Wy multiply elements

-14x^2+6x+(-4x)=0

We get rid of parentheses

-14x^2+6x-4x=0

We add all the numbers together, and all the variables

-14x^2+2x=0

a = -14; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-14)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-14}=\frac{-4}{-28}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-14}=\frac{0}{-28}
=0
$