3(6m-17)m=17

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

3(6m-17)m=17

We move all terms to the left:

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

We multiply parentheses

18m^2-51m-17=0

a = 18; b = -51; c = -17;
Δ = b2-4ac
Δ = -512-4·18·(-17)
Δ = 3825
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:

$\sqrt{\Delta}=\sqrt{3825}=\sqrt{225*17}=\sqrt{225}*\sqrt{17}=15\sqrt{17}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-15\sqrt{17}}{2*18}=\frac{51-15\sqrt{17}}{36}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+15\sqrt{17}}{2*18}=\frac{51+15\sqrt{17}}{36}
$