3/x=10/4x-2

Solution for 3/x=10/4x-2 equation:

3/x=10/4x-2

We move all terms to the left:

3/x-(10/4x-2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

3/x-10/4x+2=0

We calculate fractions


12x/4x^2+(-10x)/4x^2+2=0

We multiply all the terms by the denominator


12x+(-10x)+2*4x^2=0

Wy multiply elements

8x^2+12x+(-10x)=0

We get rid of parentheses

8x^2+12x-10x=0

We add all the numbers together, and all the variables

8x^2+2x=0

a = 8; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·8·0
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*8}=\frac{-4}{16}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*8}=\frac{0}{16}
=0
$