0.5(x+4)(x-2)=27.5

Solution for 0.5(x+4)(x-2)=27.5 equation:

0.5(x+4)(x-2)=27.5

We move all terms to the left:

0.5(x+4)(x-2)-(27.5)=0

We add all the numbers together, and all the variables

0.5(x+4)(x-2)-27.5=0

We multiply parentheses ..

0.5(+x^2-2x+4x-8)-27.5=0

We multiply parentheses

0.5x^2-1x+2x-4-27.5=0

We add all the numbers together, and all the variables

0.5x^2+x-31.5=0

a = 0.5; b = 1; c = -31.5;
Δ = b2-4ac
Δ = 12-4·0.5·(-31.5)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-8}{2*0.5}=\frac{-9}{1}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+8}{2*0.5}=\frac{7}{1}
=7
$