6f^2-81=0

Solution for 6f^2-81=0 equation:

6f^2-81=0

a = 6; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·6·(-81)
Δ = 1944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{6}}{2*6}=\frac{0-18\sqrt{6}}{12}
=-\frac{18\sqrt{6}}{12}
=-\frac{3\sqrt{6}}{2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{6}}{2*6}=\frac{0+18\sqrt{6}}{12}
=\frac{18\sqrt{6}}{12}
=\frac{3\sqrt{6}}{2}
$