6m^2+24m+7=0

Solution for 6m^2+24m+7=0 equation:

6m^2+24m+7=0

a = 6; b = 24; c = +7;
Δ = b2-4ac
Δ = 242-4·6·7
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{102}}{2*6}=\frac{-24-2\sqrt{102}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{102}}{2*6}=\frac{-24+2\sqrt{102}}{12}
$