64/(3x-4)=x

Solution for 64/(3x-4)=x equation:

64/(3x-4)=x

We move all terms to the left:

64/(3x-4)-(x)=0


Domain of the equation: (3x-4)!=0

We move all terms containing x to the left, all other terms to the right

3x!=4

x!=4/3

x!=1+1/3

x∈R


We add all the numbers together, and all the variables

-1x+64/(3x-4)=0

We multiply all the terms by the denominator


-1x*(3x-4)+64=0

We multiply parentheses

-3x^2+4x+64=0

a = -3; b = 4; c = +64;
Δ = b2-4ac
Δ = 42-4·(-3)·64
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-28}{2*-3}=\frac{-32}{-6}
=5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+28}{2*-3}=\frac{24}{-6}
=-4
$