8m^2-24=21

Solution for 8m^2-24=21 equation:

8m^2-24=21

We move all terms to the left:

8m^2-24-(21)=0

We add all the numbers together, and all the variables

8m^2-45=0

a = 8; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·8·(-45)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*8}=\frac{0-12\sqrt{10}}{16}
=-\frac{12\sqrt{10}}{16}
=-\frac{3\sqrt{10}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*8}=\frac{0+12\sqrt{10}}{16}
=\frac{12\sqrt{10}}{16}
=\frac{3\sqrt{10}}{4}
$