x^2=81/256

Solution for x^2=81/256 equation:

x^2=81/256

We move all terms to the left:

x^2-(81/256)=0

We add all the numbers together, and all the variables

x^2-(+81/256)=0

We get rid of parentheses

x^2-81/256=0

We multiply all the terms by the denominator


x^2*256-81=0

Wy multiply elements

256x^2-81=0

a = 256; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·256·(-81)
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-288}{2*256}=\frac{-288}{512}
=-9/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+288}{2*256}=\frac{288}{512}
=9/16
$