14.4=d+0.5d^2

Solution for 14.4=d+0.5d^2 equation:

14.4=d+0.5d^2

We move all terms to the left:

14.4-(d+0.5d^2)=0

We get rid of parentheses

-0.5d^2-d+14.4=0

We add all the numbers together, and all the variables

-0.5d^2-1d+14.4=0

a = -0.5; b = -1; c = +14.4;
Δ = b2-4ac
Δ = -12-4·(-0.5)·14.4
Δ = 29.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{29.8}}{2*-0.5}=\frac{1-\sqrt{29.8}}{-1}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{29.8}}{2*-0.5}=\frac{1+\sqrt{29.8}}{-1}
$