5n^2-29n+25=5

Solution for 5n^2-29n+25=5 equation:

5n^2-29n+25=5

We move all terms to the left:

5n^2-29n+25-(5)=0

We add all the numbers together, and all the variables

5n^2-29n+20=0

a = 5; b = -29; c = +20;
Δ = b2-4ac
Δ = -292-4·5·20
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-21}{2*5}=\frac{8}{10}
=4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+21}{2*5}=\frac{50}{10}
=5
$