3m(m-4)=61

Solution for 3m(m-4)=61 equation:

3m(m-4)=61

We move all terms to the left:

3m(m-4)-(61)=0

We multiply parentheses

3m^2-12m-61=0

a = 3; b = -12; c = -61;
Δ = b2-4ac
Δ = -122-4·3·(-61)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{219}}{2*3}=\frac{12-2\sqrt{219}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{219}}{2*3}=\frac{12+2\sqrt{219}}{6}
$