2/3x-3=-x-13

Solution for 2/3x-3=-x-13 equation:

2/3x-3=-x-13

We move all terms to the left:

2/3x-3-(-x-13)=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-(-1x-13)-3=0

We get rid of parentheses

2/3x+1x+13-3=0

We multiply all the terms by the denominator


1x*3x+13*3x-3*3x+2=0

Wy multiply elements

3x^2+39x-9x+2=0

We add all the numbers together, and all the variables

3x^2+30x+2=0

a = 3; b = 30; c = +2;
Δ = b2-4ac
Δ = 302-4·3·2
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{219}}{2*3}=\frac{-30-2\sqrt{219}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{219}}{2*3}=\frac{-30+2\sqrt{219}}{6}
$