0.5x^2-x=24

Solution for 0.5x^2-x=24 equation:

0.5x^2-x=24

We move all terms to the left:

0.5x^2-x-(24)=0

We add all the numbers together, and all the variables

0.5x^2-1x-24=0

a = 0.5; b = -1; c = -24;
Δ = b2-4ac
Δ = -12-4·0.5·(-24)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*0.5}=\frac{-6}{1}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*0.5}=\frac{8}{1}
=8
$