-2/3x+3=2x-5

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

-2/3x+3=2x-5

We move all terms to the left:

-2/3x+3-(2x-5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-2/3x-2x+5+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+15x+9x-2=0

We add all the numbers together, and all the variables

-6x^2+24x-2=0

a = -6; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·(-6)·(-2)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{33}}{2*-6}=\frac{-24-4\sqrt{33}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{33}}{2*-6}=\frac{-24+4\sqrt{33}}{-12}
$