6m^2-9=291

Solution for 6m^2-9=291 equation:

6m^2-9=291

We move all terms to the left:

6m^2-9-(291)=0

We add all the numbers together, and all the variables

6m^2-300=0

a = 6; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·6·(-300)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*6}=\frac{0-60\sqrt{2}}{12}
=-\frac{60\sqrt{2}}{12}
=-5\sqrt{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*6}=\frac{0+60\sqrt{2}}{12}
=\frac{60\sqrt{2}}{12}
=5\sqrt{2}
$