2m^2-11=2m

Solution for 2m^2-11=2m equation:

2m^2-11=2m

We move all terms to the left:

2m^2-11-(2m)=0

a = 2; b = -2; c = -11;
Δ = b2-4ac
Δ = -22-4·2·(-11)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{23}}{2*2}=\frac{2-2\sqrt{23}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{23}}{2*2}=\frac{2+2\sqrt{23}}{4}
$