2m^2-9=65

Solution for 2m^2-9=65 equation:

2m^2-9=65

We move all terms to the left:

2m^2-9-(65)=0

We add all the numbers together, and all the variables

2m^2-74=0

a = 2; b = 0; c = -74;
Δ = b2-4ac
Δ = 02-4·2·(-74)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{37}}{2*2}=\frac{0-4\sqrt{37}}{4}
=-\frac{4\sqrt{37}}{4}
=-\sqrt{37}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{37}}{2*2}=\frac{0+4\sqrt{37}}{4}
=\frac{4\sqrt{37}}{4}
=\sqrt{37}
$