x^2=53/11

Solution for x^2=53/11 equation:

x^2=53/11

We move all terms to the left:

x^2-(53/11)=0

We add all the numbers together, and all the variables

x^2-(+53/11)=0

We get rid of parentheses

x^2-53/11=0

We multiply all the terms by the denominator


x^2*11-53=0

Wy multiply elements

11x^2-53=0

a = 11; b = 0; c = -53;
Δ = b2-4ac
Δ = 02-4·11·(-53)
Δ = 2332
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:

$\sqrt{\Delta}=\sqrt{2332}=\sqrt{4*583}=\sqrt{4}*\sqrt{583}=2\sqrt{583}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{583}}{2*11}=\frac{0-2\sqrt{583}}{22}
=-\frac{2\sqrt{583}}{22}
=-\frac{\sqrt{583}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{583}}{2*11}=\frac{0+2\sqrt{583}}{22}
=\frac{2\sqrt{583}}{22}
=\frac{\sqrt{583}}{11}
$