1+4x-0.2x^2=1+8x-0.6x^2

Solution for 1+4x-0.2x^2=1+8x-0.6x^2 equation:

1+4x-0.2x^2=1+8x-0.6x^2

We move all terms to the left:

1+4x-0.2x^2-(1+8x-0.6x^2)=0

We get rid of parentheses

-0.2x^2+0.6x^2-8x+4x-1+1=0

We add all the numbers together, and all the variables

0.4x^2-4x=0

a = 0.4; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·0.4·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*0.4}=\frac{0}{0.8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*0.4}=\frac{8}{0.8}
=10
$