40=m2+16

Solution for 40=m2+16 equation:

40=m2+16

We move all terms to the left:

40-(m2+16)=0

We add all the numbers together, and all the variables

-(+m^2+16)+40=0

We get rid of parentheses

-m^2-16+40=0

We add all the numbers together, and all the variables

-1m^2+24=0

a = -1; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-1)·24
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-1}=\frac{0-4\sqrt{6}}{-2}
=-\frac{4\sqrt{6}}{-2}
=-\frac{2\sqrt{6}}{-1}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-1}=\frac{0+4\sqrt{6}}{-2}
=\frac{4\sqrt{6}}{-2}
=\frac{2\sqrt{6}}{-1}
$