h^2+3/7=12

Solution for h^2+3/7=12 equation:

h^2+3/7=12

We move all terms to the left:

h^2+3/7-(12)=0

determiningTheFunctionDomain
h^2-12+3/7=0

We multiply all the terms by the denominator


h^2*7+3-12*7=0

We add all the numbers together, and all the variables

h^2*7-81=0

Wy multiply elements

7h^2-81=0

a = 7; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·7·(-81)
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{7}}{2*7}=\frac{0-18\sqrt{7}}{14}
=-\frac{18\sqrt{7}}{14}
=-\frac{9\sqrt{7}}{7}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{7}}{2*7}=\frac{0+18\sqrt{7}}{14}
=\frac{18\sqrt{7}}{14}
=\frac{9\sqrt{7}}{7}
$