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

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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} $

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