3m(m-2)-(m^2+1)=0

Solution for 3m(m-2)-(m^2+1)=0 equation:

3m(m-2)-(m^2+1)=0

We multiply parentheses

3m^2-6m-(m^2+1)=0

We get rid of parentheses

3m^2-m^2-6m-1=0

We add all the numbers together, and all the variables

2m^2-6m-1=0

a = 2; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·2·(-1)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{11}}{2*2}=\frac{6-2\sqrt{11}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{11}}{2*2}=\frac{6+2\sqrt{11}}{4}
$