m^2=5m-1

Solution for m^2=5m-1 equation:

m^2=5m-1

We move all terms to the left:

m^2-(5m-1)=0

We get rid of parentheses

m^2-5m+1=0

a = 1; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·1·1
Δ = 21
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{-(-5)-\sqrt{21}}{2*1}=\frac{5-\sqrt{21}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{21}}{2*1}=\frac{5+\sqrt{21}}{2}
$