2/3x-8+x=21-3x-9

Solution for 2/3x-8+x=21-3x-9 equation:

2/3x-8+x=21-3x-9

We move all terms to the left:

2/3x-8+x-(21-3x-9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+x-(-3x+12)-8=0

We add all the numbers together, and all the variables

x+2/3x-(-3x+12)-8=0

We get rid of parentheses

x+2/3x+3x-12-8=0

We multiply all the terms by the denominator


x*3x+3x*3x-12*3x-8*3x+2=0

Wy multiply elements

3x^2+9x^2-36x-24x+2=0

We add all the numbers together, and all the variables

12x^2-60x+2=0

a = 12; b = -60; c = +2;
Δ = b2-4ac
Δ = -602-4·12·2
Δ = 3504
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:

$\sqrt{\Delta}=\sqrt{3504}=\sqrt{16*219}=\sqrt{16}*\sqrt{219}=4\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{219}}{2*12}=\frac{60-4\sqrt{219}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{219}}{2*12}=\frac{60+4\sqrt{219}}{24}
$