(x-0.5)(x-3)=0

Solution for (x-0.5)(x-3)=0 equation:

(x-0.5)(x-3)=0

We multiply parentheses ..

(+x^2-3x-0.5x+1.5)=0

We get rid of parentheses

x^2-3x-0.5x+1.5=0

We add all the numbers together, and all the variables

x^2-3.5x+1.5=0

a = 1; b = -3.5; c = +1.5;
Δ = b2-4ac
Δ = -3.52-4·1·1.5
Δ = 6.25
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{-(-3.5)-\sqrt{6.25}}{2*1}=\frac{3.5-\sqrt{6.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.5)+\sqrt{6.25}}{2*1}=\frac{3.5+\sqrt{6.25}}{2}
$