6m^2-14m-4=0

Solution for 6m^2-14m-4=0 equation:

6m^2-14m-4=0

a = 6; b = -14; c = -4;
Δ = b2-4ac
Δ = -142-4·6·(-4)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{73}}{2*6}=\frac{14-2\sqrt{73}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{73}}{2*6}=\frac{14+2\sqrt{73}}{12}
$