2m^2-m-3=2

Solution for 2m^2-m-3=2 equation:

2m^2-m-3=2

We move all terms to the left:

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

We add all the numbers together, and all the variables

2m^2-1m-5=0

a = 2; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·2·(-5)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{41}}{2*2}=\frac{1-\sqrt{41}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*2}=\frac{1+\sqrt{41}}{4}
$