2m2-4m=3

Solution for 2m2-4m=3 equation:

2m^2-4m=3

We move all terms to the left:

2m^2-4m-(3)=0

a = 2; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·2·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*2}=\frac{4-2\sqrt{10}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*2}=\frac{4+2\sqrt{10}}{4}
$