5m^2-9=471

Solution for 5m^2-9=471 equation:

5m^2-9=471

We move all terms to the left:

5m^2-9-(471)=0

We add all the numbers together, and all the variables

5m^2-480=0

a = 5; b = 0; c = -480;
Δ = b2-4ac
Δ = 02-4·5·(-480)
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*5}=\frac{0-40\sqrt{6}}{10}
=-\frac{40\sqrt{6}}{10}
=-4\sqrt{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*5}=\frac{0+40\sqrt{6}}{10}
=\frac{40\sqrt{6}}{10}
=4\sqrt{6}
$