x+6=4/3x-3

Solution for x+6=4/3x-3 equation:

x+6=4/3x-3

We move all terms to the left:

x+6-(4/3x-3)=0


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

x∈R


We get rid of parentheses

x-4/3x+3+6=0

We multiply all the terms by the denominator


x*3x+3*3x+6*3x-4=0

Wy multiply elements

3x^2+9x+18x-4=0

We add all the numbers together, and all the variables

3x^2+27x-4=0

a = 3; b = 27; c = -4;
Δ = b2-4ac
Δ = 272-4·3·(-4)
Δ = 777
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{777}}{2*3}=\frac{-27-\sqrt{777}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{777}}{2*3}=\frac{-27+\sqrt{777}}{6}
$