2/3x-x=-21

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

2/3x-x=-21

We move all terms to the left:

2/3x-x-(-21)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2/3x+21=0

We multiply all the terms by the denominator


-1x*3x+21*3x+2=0

Wy multiply elements

-3x^2+63x+2=0

a = -3; b = 63; c = +2;
Δ = b2-4ac
Δ = 632-4·(-3)·2
Δ = 3993
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:

$\sqrt{\Delta}=\sqrt{3993}=\sqrt{121*33}=\sqrt{121}*\sqrt{33}=11\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-11\sqrt{33}}{2*-3}=\frac{-63-11\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+11\sqrt{33}}{2*-3}=\frac{-63+11\sqrt{33}}{-6}
$