5x-4=2/3x

Solution for 5x-4=2/3x equation:

5x-4=2/3x

We move all terms to the left:

5x-4-(2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+2/3x)-4=0

We get rid of parentheses

5x-2/3x-4=0

We multiply all the terms by the denominator


5x*3x-4*3x-2=0

Wy multiply elements

15x^2-12x-2=0

a = 15; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·15·(-2)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*15}=\frac{12-2\sqrt{66}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*15}=\frac{12+2\sqrt{66}}{30}
$