5=1/3q^2

Solution for 5=1/3q^2 equation:

5=1/3q^2

We move all terms to the left:

5-(1/3q^2)=0


Domain of the equation: 3q^2)!=0

q!=0/1

q!=0

q∈R


We get rid of parentheses

-1/3q^2+5=0

We multiply all the terms by the denominator


5*3q^2-1=0

Wy multiply elements

15q^2-1=0

a = 15; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·15·(-1)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*15}=\frac{0-2\sqrt{15}}{30}
=-\frac{2\sqrt{15}}{30}
=-\frac{\sqrt{15}}{15}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*15}=\frac{0+2\sqrt{15}}{30}
=\frac{2\sqrt{15}}{30}
=\frac{\sqrt{15}}{15}
$