3m^2=7^4

Solution for 3m^2=7^4 equation:

3m^2=7^4

We move all terms to the left:

3m^2-(7^4)=0

We add all the numbers together, and all the variables

3m^2-2401=0

a = 3; b = 0; c = -2401;
Δ = b2-4ac
Δ = 02-4·3·(-2401)
Δ = 28812
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28812}=\sqrt{9604*3}=\sqrt{9604}*\sqrt{3}=98\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-98\sqrt{3}}{2*3}=\frac{0-98\sqrt{3}}{6}
=-\frac{98\sqrt{3}}{6}
=-\frac{49\sqrt{3}}{3}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+98\sqrt{3}}{2*3}=\frac{0+98\sqrt{3}}{6}
=\frac{98\sqrt{3}}{6}
=\frac{49\sqrt{3}}{3}
$