14=1/3b2

Solution for 14=1/3b2 equation:

14=1/3b^2

We move all terms to the left:

14-(1/3b^2)=0


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

b!=0/1

b!=0

b∈R


We get rid of parentheses

-1/3b^2+14=0

We multiply all the terms by the denominator


14*3b^2-1=0

Wy multiply elements

42b^2-1=0

a = 42; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·42·(-1)
Δ = 168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*42}=\frac{0-2\sqrt{42}}{84}
=-\frac{2\sqrt{42}}{84}
=-\frac{\sqrt{42}}{42}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*42}=\frac{0+2\sqrt{42}}{84}
=\frac{2\sqrt{42}}{84}
=\frac{\sqrt{42}}{42}
$