x^2=55/36

Solution for x^2=55/36 equation:

x^2=55/36

We move all terms to the left:

x^2-(55/36)=0

We add all the numbers together, and all the variables

x^2-(+55/36)=0

We get rid of parentheses

x^2-55/36=0

We multiply all the terms by the denominator


x^2*36-55=0

Wy multiply elements

36x^2-55=0

a = 36; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·36·(-55)
Δ = 7920
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:

$\sqrt{\Delta}=\sqrt{7920}=\sqrt{144*55}=\sqrt{144}*\sqrt{55}=12\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{55}}{2*36}=\frac{0-12\sqrt{55}}{72}
=-\frac{12\sqrt{55}}{72}
=-\frac{\sqrt{55}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{55}}{2*36}=\frac{0+12\sqrt{55}}{72}
=\frac{12\sqrt{55}}{72}
=\frac{\sqrt{55}}{6}
$