(1/3)(x+27)=4

Solution for (1/3)(x+27)=4 equation:

(1/3)(x+27)=4

We move all terms to the left:

(1/3)(x+27)-(4)=0


Domain of the equation: 3)(x+27)!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)(x+27)-4=0

We multiply parentheses ..

(+x^2+1/3*27)-4=0

We multiply all the terms by the denominator


(+x^2+1-4*3*27)=0

We get rid of parentheses

x^2+1-4*3*27=0

We add all the numbers together, and all the variables

x^2-323=0

a = 1; b = 0; c = -323;
Δ = b2-4ac
Δ = 02-4·1·(-323)
Δ = 1292
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:

$\sqrt{\Delta}=\sqrt{1292}=\sqrt{4*323}=\sqrt{4}*\sqrt{323}=2\sqrt{323}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{323}}{2*1}=\frac{0-2\sqrt{323}}{2}
=-\frac{2\sqrt{323}}{2}
=-\sqrt{323}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{323}}{2*1}=\frac{0+2\sqrt{323}}{2}
=\frac{2\sqrt{323}}{2}
=\sqrt{323}
$