x(3/4)=8/27

Solution for x(3/4)=8/27 equation:

x(3/4)=8/27

We move all terms to the left:

x(3/4)-(8/27)=0

We add all the numbers together, and all the variables

x(+3/4)-(+8/27)=0

We multiply parentheses

3x^2-(+8/27)=0

We get rid of parentheses

3x^2-8/27=0

We multiply all the terms by the denominator


3x^2*27-8=0

Wy multiply elements

81x^2-8=0

a = 81; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·81·(-8)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{2}}{2*81}=\frac{0-36\sqrt{2}}{162}
=-\frac{36\sqrt{2}}{162}
=-\frac{2\sqrt{2}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*81}=\frac{0+36\sqrt{2}}{162}
=\frac{36\sqrt{2}}{162}
=\frac{2\sqrt{2}}{9}
$