1-6m+3m^2=m^2+3m+4

Solution for 1-6m+3m^2=m^2+3m+4 equation:

1-6m+3m^2=m^2+3m+4

We move all terms to the left:

1-6m+3m^2-(m^2+3m+4)=0

We get rid of parentheses

3m^2-m^2-6m-3m-4+1=0

We add all the numbers together, and all the variables

2m^2-9m-3=0

a = 2; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·2·(-3)
Δ = 105
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{-(-9)-\sqrt{105}}{2*2}=\frac{9-\sqrt{105}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*2}=\frac{9+\sqrt{105}}{4}
$