3(6m-17)m=5

Solution for 3(6m-17)m=5 equation:

3(6m-17)m=5

We move all terms to the left:

3(6m-17)m-(5)=0

We multiply parentheses

18m^2-51m-5=0

a = 18; b = -51; c = -5;
Δ = b2-4ac
Δ = -512-4·18·(-5)
Δ = 2961
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:

$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{329}}{2*18}=\frac{51-3\sqrt{329}}{36}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{329}}{2*18}=\frac{51+3\sqrt{329}}{36}
$