5=0.8x+0.8x^2

Solution for 5=0.8x+0.8x^2 equation:

5=0.8x+0.8x^2

We move all terms to the left:

5-(0.8x+0.8x^2)=0

We get rid of parentheses

-0.8x^2-0.8x+5=0

a = -0.8; b = -0.8; c = +5;
Δ = b2-4ac
Δ = -0.82-4·(-0.8)·5
Δ = 16.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.8)-\sqrt{16.64}}{2*-0.8}=\frac{0.8-\sqrt{16.64}}{-1.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.8)+\sqrt{16.64}}{2*-0.8}=\frac{0.8+\sqrt{16.64}}{-1.6}
$