(6m-17)m=5

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

(6m-17)m=5

We move all terms to the left:

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

We multiply parentheses

6m^2-17m-5=0

a = 6; b = -17; c = -5;
Δ = b2-4ac
Δ = -172-4·6·(-5)
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{409}}{2*6}=\frac{17-\sqrt{409}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{409}}{2*6}=\frac{17+\sqrt{409}}{12}
$