x2+1.8x+0.81=420.25

Solution for x2+1.8x+0.81=420.25 equation:

x2+1.8x+0.81=420.25

We move all terms to the left:

x2+1.8x+0.81-(420.25)=0

We add all the numbers together, and all the variables

x^2+1.8x-419.44=0

a = 1; b = 1.8; c = -419.44;
Δ = b2-4ac
Δ = 1.82-4·1·(-419.44)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.8)-41}{2*1}=\frac{-42.8}{2}
=-21+0.8/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.8)+41}{2*1}=\frac{39.2}{2}
=19+1/1.6666666666667
$