10=1/3q^2

Solution for 10=1/3q^2 equation:

10=1/3q^2

We move all terms to the left:

10-(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+10=0

We multiply all the terms by the denominator


10*3q^2-1=0

Wy multiply elements

30q^2-1=0

a = 30; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·30·(-1)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*30}=\frac{0-2\sqrt{30}}{60}
=-\frac{2\sqrt{30}}{60}
=-\frac{\sqrt{30}}{30}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*30}=\frac{0+2\sqrt{30}}{60}
=\frac{2\sqrt{30}}{60}
=\frac{\sqrt{30}}{30}
$