6m^2+8m-3=0

Solution for 6m^2+8m-3=0 equation:

6m^2+8m-3=0

a = 6; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·6·(-3)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{34}}{2*6}=\frac{-8-2\sqrt{34}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{34}}{2*6}=\frac{-8+2\sqrt{34}}{12}
$