2/3x+9=2123x+9=21

Solution for 2/3x+9=2123x+9=21 equation:

2/3x+9=2123x+9=21

We move all terms to the left:

2/3x+9-(2123x+9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-2123x-9+9=0

We multiply all the terms by the denominator


-2123x*3x-9*3x+9*3x+2=0

Wy multiply elements

-6369x^2-27x+27x+2=0

We add all the numbers together, and all the variables

-6369x^2+2=0

a = -6369; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-6369)·2
Δ = 50952
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:

$\sqrt{\Delta}=\sqrt{50952}=\sqrt{4*12738}=\sqrt{4}*\sqrt{12738}=2\sqrt{12738}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{12738}}{2*-6369}=\frac{0-2\sqrt{12738}}{-12738}
=-\frac{2\sqrt{12738}}{-12738}
=-\frac{\sqrt{12738}}{-6369}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{12738}}{2*-6369}=\frac{0+2\sqrt{12738}}{-12738}
=\frac{2\sqrt{12738}}{-12738}
=\frac{\sqrt{12738}}{-6369}
$