3m^2-4m-186=0

Solution for 3m^2-4m-186=0 equation:

3m^2-4m-186=0

a = 3; b = -4; c = -186;
Δ = b2-4ac
Δ = -42-4·3·(-186)
Δ = 2248
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:

$\sqrt{\Delta}=\sqrt{2248}=\sqrt{4*562}=\sqrt{4}*\sqrt{562}=2\sqrt{562}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{562}}{2*3}=\frac{4-2\sqrt{562}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{562}}{2*3}=\frac{4+2\sqrt{562}}{6}
$