2/3*3x+6)=4x+3

Solution for 2/3*3x+6)=4x+3 equation:

2/3*3x+6)=4x+3

We move all terms to the left:

2/3*3x+6)-(4x+3)=0


Domain of the equation: 3*3x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3*3x+6)-(4x=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-4x*3*3x+8=0

Wy multiply elements

-36x^2*3+8=0

Wy multiply elements

-108x^2+8=0

a = -108; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-108)·8
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*-108}=\frac{0-24\sqrt{6}}{-216}
=-\frac{24\sqrt{6}}{-216}
=-\frac{\sqrt{6}}{-9}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*-108}=\frac{0+24\sqrt{6}}{-216}
=\frac{24\sqrt{6}}{-216}
=\frac{\sqrt{6}}{-9}$