7/x-4x/2x-3=-2

Solution for 7/x-4x/2x-3=-2 equation:

7/x-4x/2x-3=-2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7/x-4x/2x-1=0

We calculate fractions


(-4x^2)/2x^2+14x/2x^2-1=0

We multiply all the terms by the denominator


(-4x^2)+14x-1*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2+14x=0

a = -6; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-6)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-6}=\frac{-28}{-12}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-6}=\frac{0}{-12}
=0
$