(a-0.5)(a-0.3)=0

Solution for (a-0.5)(a-0.3)=0 equation:

(a-0.5)(a-0.3)=0

We multiply parentheses ..

(+a^2-0.3a-0.5a+0.15)=0

We get rid of parentheses

a^2-0.3a-0.5a+0.15=0

We add all the numbers together, and all the variables

a^2-0.8a+0.15=0

a = 1; b = -0.8; c = +0.15;
Δ = b2-4ac
Δ = -0.82-4·1·0.15
Δ = 0.04
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{-(-0.8)-\sqrt{0.04}}{2*1}=\frac{0.8-\sqrt{0.04}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.8)+\sqrt{0.04}}{2*1}=\frac{0.8+\sqrt{0.04}}{2}
$