X-2/3x-1/3x=21

Solution for X-2/3x-1/3x=21 equation:

X-2/3X-1/3X=21

We move all terms to the left:

X-2/3X-1/3X-(21)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-21*3X-2-1=0

We add all the numbers together, and all the variables

X*3X-21*3X-3=0

Wy multiply elements

3X^2-63X-3=0

a = 3; b = -63; c = -3;
Δ = b2-4ac
Δ = -632-4·3·(-3)
Δ = 4005
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:

$\sqrt{\Delta}=\sqrt{4005}=\sqrt{9*445}=\sqrt{9}*\sqrt{445}=3\sqrt{445}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{445}}{2*3}=\frac{63-3\sqrt{445}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{445}}{2*3}=\frac{63+3\sqrt{445}}{6}
$