4/x=2x-3

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

4/x=2x-3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-2x+3=0

We multiply all the terms by the denominator


-2x*x+3*x+4=0

We add all the numbers together, and all the variables

3x-2x*x+4=0

Wy multiply elements

-2x^2+3x+4=0

a = -2; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-2)·4
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{41}}{2*-2}=\frac{-3-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*-2}=\frac{-3+\sqrt{41}}{-4}
$