6m^2-4m-7=0

Solution for 6m^2-4m-7=0 equation:

6m^2-4m-7=0

a = 6; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·6·(-7)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{46}}{2*6}=\frac{4-2\sqrt{46}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{46}}{2*6}=\frac{4+2\sqrt{46}}{12}
$