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

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