8m^2-9=567

Solution for 8m^2-9=567 equation:

8m^2-9=567

We move all terms to the left:

8m^2-9-(567)=0

We add all the numbers together, and all the variables

8m^2-576=0

a = 8; b = 0; c = -576;
Δ = b2-4ac
Δ = 02-4·8·(-576)
Δ = 18432
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:

$\sqrt{\Delta}=\sqrt{18432}=\sqrt{9216*2}=\sqrt{9216}*\sqrt{2}=96\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96\sqrt{2}}{2*8}=\frac{0-96\sqrt{2}}{16}
=-\frac{96\sqrt{2}}{16}
=-6\sqrt{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96\sqrt{2}}{2*8}=\frac{0+96\sqrt{2}}{16}
=\frac{96\sqrt{2}}{16}
=6\sqrt{2}
$