3(5m-4)m=2

Solution for 3(5m-4)m=2 equation:

3(5m-4)m=2

We move all terms to the left:

3(5m-4)m-(2)=0

We multiply parentheses

15m^2-12m-2=0

a = 15; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·15·(-2)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*15}=\frac{12-2\sqrt{66}}{30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*15}=\frac{12+2\sqrt{66}}{30}
$