x^2=46/121

Solution for x^2=46/121 equation:

x^2=46/121

We move all terms to the left:

x^2-(46/121)=0

We add all the numbers together, and all the variables

x^2-(+46/121)=0

We get rid of parentheses

x^2-46/121=0

We multiply all the terms by the denominator


x^2*121-46=0

Wy multiply elements

121x^2-46=0

a = 121; b = 0; c = -46;
Δ = b2-4ac
Δ = 02-4·121·(-46)
Δ = 22264
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:

$\sqrt{\Delta}=\sqrt{22264}=\sqrt{484*46}=\sqrt{484}*\sqrt{46}=22\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{46}}{2*121}=\frac{0-22\sqrt{46}}{242}
=-\frac{22\sqrt{46}}{242}
=-\frac{\sqrt{46}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{46}}{2*121}=\frac{0+22\sqrt{46}}{242}
=\frac{22\sqrt{46}}{242}
=\frac{\sqrt{46}}{11}
$