3m^2+7=310

Solution for 3m^2+7=310 equation:

3m^2+7=310

We move all terms to the left:

3m^2+7-(310)=0

We add all the numbers together, and all the variables

3m^2-303=0

a = 3; b = 0; c = -303;
Δ = b2-4ac
Δ = 02-4·3·(-303)
Δ = 3636
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:

$\sqrt{\Delta}=\sqrt{3636}=\sqrt{36*101}=\sqrt{36}*\sqrt{101}=6\sqrt{101}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{101}}{2*3}=\frac{0-6\sqrt{101}}{6}
=-\frac{6\sqrt{101}}{6}
=-\sqrt{101}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{101}}{2*3}=\frac{0+6\sqrt{101}}{6}
=\frac{6\sqrt{101}}{6}
=\sqrt{101}
$