6m^2+42m=60

Solution for 6m^2+42m=60 equation:

6m^2+42m=60

We move all terms to the left:

6m^2+42m-(60)=0

a = 6; b = 42; c = -60;
Δ = b2-4ac
Δ = 422-4·6·(-60)
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{89}}{2*6}=\frac{-42-6\sqrt{89}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{89}}{2*6}=\frac{-42+6\sqrt{89}}{12}
$