4x^2-12x+9/9-6x=3-2x/3

Solution for 4x^2-12x+9/9-6x=3-2x/3 equation:

4x^2-12x+9/9-6x=3-2x/3

We move all terms to the left:

4x^2-12x+9/9-6x-(3-2x/3)=0

We add all the numbers together, and all the variables

4x^2-12x-6x-(-2x/3+3)+9/9=0

We add all the numbers together, and all the variables

4x^2-18x-(-2x/3+3)+1=0

We get rid of parentheses

4x^2-18x+2x/3-3+1=0

We multiply all the terms by the denominator


4x^2*3-18x*3+2x-3*3+1*3=0

We add all the numbers together, and all the variables

4x^2*3+2x-18x*3-6=0

Wy multiply elements

12x^2+2x-54x-6=0

We add all the numbers together, and all the variables

12x^2-52x-6=0

a = 12; b = -52; c = -6;
Δ = b2-4ac
Δ = -522-4·12·(-6)
Δ = 2992
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:

$\sqrt{\Delta}=\sqrt{2992}=\sqrt{16*187}=\sqrt{16}*\sqrt{187}=4\sqrt{187}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{187}}{2*12}=\frac{52-4\sqrt{187}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{187}}{2*12}=\frac{52+4\sqrt{187}}{24}
$