0,5(x-3)(x+1)=1

Solution for 0,5(x-3)(x+1)=1 equation:

0.5(x-3)(x+1)=1

We move all terms to the left:

0.5(x-3)(x+1)-(1)=0

We multiply parentheses ..

0.5(+x^2+x-3x-3)-1=0

We multiply parentheses

0.5x^2+0.5x-1.5x-1.5-1=0

We add all the numbers together, and all the variables

0.5x^2-1x-2.5=0

a = 0.5; b = -1; c = -2.5;
Δ = b2-4ac
Δ = -12-4·0.5·(-2.5)
Δ = 6
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{-(-1)-\sqrt{6}}{2*0.5}=\frac{1-\sqrt{6}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{6}}{2*0.5}=\frac{1+\sqrt{6}}{1}
$