4/3x+2=9x-1

Solution for 4/3x+2=9x-1 equation:

4/3x+2=9x-1

We move all terms to the left:

4/3x+2-(9x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-9x+1+2=0

We multiply all the terms by the denominator


-9x*3x+1*3x+2*3x+4=0

Wy multiply elements

-27x^2+3x+6x+4=0

We add all the numbers together, and all the variables

-27x^2+9x+4=0

a = -27; b = 9; c = +4;
Δ = b2-4ac
Δ = 92-4·(-27)·4
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{57}}{2*-27}=\frac{-9-3\sqrt{57}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{57}}{2*-27}=\frac{-9+3\sqrt{57}}{-54}
$