(x+.5)(x+1)=9

Solution for (x+.5)(x+1)=9 equation:

(x+.5)(x+1)=9

We move all terms to the left:

(x+.5)(x+1)-(9)=0

We add all the numbers together, and all the variables

(x+0.5)(x+1)-9=0

We multiply parentheses ..

(+x^2+x+0.5x+0.5)-9=0

We get rid of parentheses

x^2+x+0.5x+0.5-9=0

We add all the numbers together, and all the variables

x^2+1.5x-8.5=0

a = 1; b = 1.5; c = -8.5;
Δ = b2-4ac
Δ = 1.52-4·1·(-8.5)
Δ = 36.25
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{-(1.5)-\sqrt{36.25}}{2*1}=\frac{-1.5-\sqrt{36.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{36.25}}{2*1}=\frac{-1.5+\sqrt{36.25}}{2}
$