12m^2-10m=24

Solution for 12m^2-10m=24 equation:

12m^2-10m=24

We move all terms to the left:

12m^2-10m-(24)=0

a = 12; b = -10; c = -24;
Δ = b2-4ac
Δ = -102-4·12·(-24)
Δ = 1252
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:

$\sqrt{\Delta}=\sqrt{1252}=\sqrt{4*313}=\sqrt{4}*\sqrt{313}=2\sqrt{313}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{313}}{2*12}=\frac{10-2\sqrt{313}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{313}}{2*12}=\frac{10+2\sqrt{313}}{24}
$