0=-0.5d^2+6d+7

Solution for 0=-0.5d^2+6d+7 equation:

0=-0.5d^2+6d+7

We move all terms to the left:

0-(-0.5d^2+6d+7)=0

We add all the numbers together, and all the variables

-(-0.5d^2+6d+7)=0

We get rid of parentheses

0.5d^2-6d-7=0

a = 0.5; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·0.5·(-7)
Δ = 50
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{50}=\sqrt{25*2}=\sqrt{25}*\sqrt{2}=5\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-5\sqrt{2}}{2*0.5}=\frac{6-5\sqrt{2}}{1}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+5\sqrt{2}}{2*0.5}=\frac{6+5\sqrt{2}}{1}
$