-2/x=-7/2x-2

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

-2/x=-7/2x-2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

-2/x+7/2x+2=0

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

4x^2+7x-4x=0

We add all the numbers together, and all the variables

4x^2+3x=0

a = 4; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·4·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*4}=\frac{-6}{8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*4}=\frac{0}{8}
=0
$