(x2+6x+9)3/4-13=14

Solution for (x2+6x+9)3/4-13=14 equation:

(x2+6x+9)3/4-13=14

We move all terms to the left:

(x2+6x+9)3/4-13-(14)=0

We add all the numbers together, and all the variables

(+x^2+6x+9)3/4-13-14=0

We add all the numbers together, and all the variables

(+x^2+6x+9)3/4-27=0

We multiply all the terms by the denominator


(+x^2+6x+9)3-27*4=0

We add all the numbers together, and all the variables

(+x^2+6x+9)3-108=0

We multiply parentheses

3x^2+18x+27-108=0

We add all the numbers together, and all the variables

3x^2+18x-81=0

a = 3; b = 18; c = -81;
Δ = b2-4ac
Δ = 182-4·3·(-81)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-36}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+36}{2*3}=\frac{18}{6}
=3
$