a^2=64/81

Solution for a^2=64/81 equation:

a^2=64/81

We move all terms to the left:

a^2-(64/81)=0

We add all the numbers together, and all the variables

a^2-(+64/81)=0

We get rid of parentheses

a^2-64/81=0

We multiply all the terms by the denominator


a^2*81-64=0

Wy multiply elements

81a^2-64=0

a = 81; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·81·(-64)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144}{2*81}=\frac{-144}{162}
=-8/9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144}{2*81}=\frac{144}{162}
=8/9
$