2/3x+5=-3x-3

Solution for 2/3x+5=-3x-3 equation:

2/3x+5=-3x-3

We move all terms to the left:

2/3x+5-(-3x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x+3x+3+5=0

We multiply all the terms by the denominator


3x*3x+3*3x+5*3x+2=0

Wy multiply elements

9x^2+9x+15x+2=0

We add all the numbers together, and all the variables

9x^2+24x+2=0

a = 9; b = 24; c = +2;
Δ = b2-4ac
Δ = 242-4·9·2
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{14}}{2*9}=\frac{-24-6\sqrt{14}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{14}}{2*9}=\frac{-24+6\sqrt{14}}{18}
$