x^2=121/30

Solution for x^2=121/30 equation:

x^2=121/30

We move all terms to the left:

x^2-(121/30)=0

We add all the numbers together, and all the variables

x^2-(+121/30)=0

We get rid of parentheses

x^2-121/30=0

We multiply all the terms by the denominator


x^2*30-121=0

Wy multiply elements

30x^2-121=0

a = 30; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·30·(-121)
Δ = 14520
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:

$\sqrt{\Delta}=\sqrt{14520}=\sqrt{484*30}=\sqrt{484}*\sqrt{30}=22\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{30}}{2*30}=\frac{0-22\sqrt{30}}{60}
=-\frac{22\sqrt{30}}{60}
=-\frac{11\sqrt{30}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{30}}{2*30}=\frac{0+22\sqrt{30}}{60}
=\frac{22\sqrt{30}}{60}
=\frac{11\sqrt{30}}{30}
$