4/3x-4=5x

Solution for 4/3x-4=5x equation:

4/3x-4=5x

We move all terms to the left:

4/3x-4-(5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+4/3x-4=0

We multiply all the terms by the denominator


-5x*3x-4*3x+4=0

Wy multiply elements

-15x^2-12x+4=0

a = -15; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·(-15)·4
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{6}}{2*-15}=\frac{12-8\sqrt{6}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{6}}{2*-15}=\frac{12+8\sqrt{6}}{-30}
$