x+3=-2/3x-11

Solution for x+3=-2/3x-11 equation:

x+3=-2/3x-11

We move all terms to the left:

x+3-(-2/3x-11)=0


Domain of the equation: 3x-11)!=0

x∈R


We get rid of parentheses

x+2/3x+11+3=0

We multiply all the terms by the denominator


x*3x+11*3x+3*3x+2=0

Wy multiply elements

3x^2+33x+9x+2=0

We add all the numbers together, and all the variables

3x^2+42x+2=0

a = 3; b = 42; c = +2;
Δ = b2-4ac
Δ = 422-4·3·2
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{435}}{2*3}=\frac{-42-2\sqrt{435}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{435}}{2*3}=\frac{-42+2\sqrt{435}}{6}
$