0=-0.5(x-24)(x+14)

Solution for 0=-0.5(x-24)(x+14) equation:

0=-0.5(x-24)(x+14)

We move all terms to the left:

0-(-0.5(x-24)(x+14))=0

We add all the numbers together, and all the variables

-(-0.5(x-24)(x+14))=0

We multiply parentheses ..

-(-0.5(+x^2+14x-24x-336))=0


We calculate terms in parentheses: -(-0.5(+x^2+14x-24x-336)), so:

-0.5(+x^2+14x-24x-336)

We multiply parentheses

-0.5x^2-7x+12x+168

We add all the numbers together, and all the variables

-0.5x^2+5x+168

Back to the equation:

-(-0.5x^2+5x+168)


We get rid of parentheses

0.5x^2-5x-168=0

a = 0.5; b = -5; c = -168;
Δ = b2-4ac
Δ = -52-4·0.5·(-168)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*0.5}=\frac{-14}{1}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*0.5}=\frac{24}{1}
=24
$