a^2=-5a+1

Solution for a^2=-5a+1 equation:

a^2=-5a+1

We move all terms to the left:

a^2-(-5a+1)=0

We get rid of parentheses

a^2+5a-1=0

a = 1; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·1·(-1)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{29}}{2*1}=\frac{-5-\sqrt{29}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{29}}{2*1}=\frac{-5+\sqrt{29}}{2}
$