9m^2-10=6m

Solution for 9m^2-10=6m equation:

9m^2-10=6m

We move all terms to the left:

9m^2-10-(6m)=0

a = 9; b = -6; c = -10;
Δ = b2-4ac
Δ = -62-4·9·(-10)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{11}}{2*9}=\frac{6-6\sqrt{11}}{18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{11}}{2*9}=\frac{6+6\sqrt{11}}{18}
$