-6m2=24m-10

Solution for -6m2=24m-10 equation:

-6m^2=24m-10

We move all terms to the left:

-6m^2-(24m-10)=0

We get rid of parentheses

-6m^2-24m+10=0

a = -6; b = -24; c = +10;
Δ = b2-4ac
Δ = -242-4·(-6)·10
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{51}}{2*-6}=\frac{24-4\sqrt{51}}{-12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{51}}{2*-6}=\frac{24+4\sqrt{51}}{-12}
$