32/x=3x-4

Solution for 32/x=3x-4 equation:

32/x=3x-4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

32/x-3x+4=0

We multiply all the terms by the denominator


-3x*x+4*x+32=0

We add all the numbers together, and all the variables

4x-3x*x+32=0

Wy multiply elements

-3x^2+4x+32=0

a = -3; b = 4; c = +32;
Δ = b2-4ac
Δ = 42-4·(-3)·32
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*-3}=\frac{16}{-6}
=-2+2/3
$