X-3=5-2/3x

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

X-3=5-2/3X

We move all terms to the left:

X-3-(5-2/3X)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3X^2-15X-9X+2=0

We add all the numbers together, and all the variables

3X^2-24X+2=0

a = 3; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·3·2
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{138}}{2*3}=\frac{24-2\sqrt{138}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{138}}{2*3}=\frac{24+2\sqrt{138}}{6}
$