x^2=68/36

Solution for x^2=68/36 equation:

x^2=68/36

We move all terms to the left:

x^2-(68/36)=0

We add all the numbers together, and all the variables

x^2-(+68/36)=0

We get rid of parentheses

x^2-68/36=0

We multiply all the terms by the denominator


x^2*36-68=0

Wy multiply elements

36x^2-68=0

a = 36; b = 0; c = -68;
Δ = b2-4ac
Δ = 02-4·36·(-68)
Δ = 9792
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:

$\sqrt{\Delta}=\sqrt{9792}=\sqrt{576*17}=\sqrt{576}*\sqrt{17}=24\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{17}}{2*36}=\frac{0-24\sqrt{17}}{72}
=-\frac{24\sqrt{17}}{72}
=-\frac{\sqrt{17}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{17}}{2*36}=\frac{0+24\sqrt{17}}{72}
=\frac{24\sqrt{17}}{72}
=\frac{\sqrt{17}}{3}
$