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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+9x+27x-2=0

We add all the numbers together, and all the variables

-12x^2+36x-2=0

a = -12; b = 36; c = -2;
Δ = b2-4ac
Δ = 362-4·(-12)·(-2)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-20\sqrt{3}}{2*-12}=\frac{-36-20\sqrt{3}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+20\sqrt{3}}{2*-12}=\frac{-36+20\sqrt{3}}{-24}
$