x^2=8/9

Solution for x^2=8/9 equation:

x^2=8/9

We move all terms to the left:

x^2-(8/9)=0

We add all the numbers together, and all the variables

x^2-(+8/9)=0

We get rid of parentheses

x^2-8/9=0

We multiply all the terms by the denominator


x^2*9-8=0

Wy multiply elements

9x^2-8=0

a = 9; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·9·(-8)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*9}=\frac{0-12\sqrt{2}}{18}
=-\frac{12\sqrt{2}}{18}
=-\frac{2\sqrt{2}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*9}=\frac{0+12\sqrt{2}}{18}
=\frac{12\sqrt{2}}{18}
=\frac{2\sqrt{2}}{3}
$