4/3x+2=5x

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

4/3x+2=5x

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

-15x^2+6x+4=0

a = -15; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-15)·4
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*-15}=\frac{-6-2\sqrt{69}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*-15}=\frac{-6+2\sqrt{69}}{-30}
$