(1/3)(x+6)=16

Solution for (1/3)(x+6)=16 equation:

(1/3)(x+6)=16

We move all terms to the left:

(1/3)(x+6)-(16)=0


Domain of the equation: 3)(x+6)!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)(x+6)-16=0

We multiply parentheses ..

(+x^2+1/3*6)-16=0

We multiply all the terms by the denominator


(+x^2+1-16*3*6)=0

We get rid of parentheses

x^2+1-16*3*6=0

We add all the numbers together, and all the variables

x^2-287=0

a = 1; b = 0; c = -287;
Δ = b2-4ac
Δ = 02-4·1·(-287)
Δ = 1148
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:

$\sqrt{\Delta}=\sqrt{1148}=\sqrt{4*287}=\sqrt{4}*\sqrt{287}=2\sqrt{287}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{287}}{2*1}=\frac{0-2\sqrt{287}}{2}
=-\frac{2\sqrt{287}}{2}
=-\sqrt{287}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{287}}{2*1}=\frac{0+2\sqrt{287}}{2}
=\frac{2\sqrt{287}}{2}
=\sqrt{287}
$