5+2/3(x)=x-6

Solution for 5+2/3(x)=x-6 equation:

5+2/3(x)=x-6

We move all terms to the left:

5+2/3(x)-(x-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-x+6+5=0

We multiply all the terms by the denominator


-x*3x+6*3x+5*3x+2=0

Wy multiply elements

-3x^2+18x+15x+2=0

We add all the numbers together, and all the variables

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

a = -3; b = 33; c = +2;
Δ = b2-4ac
Δ = 332-4·(-3)·2
Δ = 1113
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{-(33)-\sqrt{1113}}{2*-3}=\frac{-33-\sqrt{1113}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1113}}{2*-3}=\frac{-33+\sqrt{1113}}{-6}
$