7/x=4/2x-3

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

7/x=4/2x-3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


14x/2x^2+(-4x)/2x^2+3=0

We multiply all the terms by the denominator


14x+(-4x)+3*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+10x=0

a = 6; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·6·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*6}=\frac{-20}{12}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*6}=\frac{0}{12}
=0
$