1/3*h^2=49

Solution for 1/3*h^2=49 equation:

1/3h^2=49

We move all terms to the left:

1/3h^2-(49)=0


Domain of the equation: 3h^2!=0

h^2!=0/3

h^2!=√0

h!=0

h∈R


We multiply all the terms by the denominator


-49*3h^2+1=0

Wy multiply elements

-147h^2+1=0

a = -147; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-147)·1
Δ = 588
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*-147}=\frac{0-14\sqrt{3}}{-294}
=-\frac{14\sqrt{3}}{-294}
=-\frac{\sqrt{3}}{-21}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*-147}=\frac{0+14\sqrt{3}}{-294}
=\frac{14\sqrt{3}}{-294}
=\frac{\sqrt{3}}{-21}
$