3.5=-2d^2+14d

Solution for 3.5=-2d^2+14d equation:

3.5=-2d^2+14d

We move all terms to the left:

3.5-(-2d^2+14d)=0

We get rid of parentheses

2d^2-14d+3.5=0

a = 2; b = -14; c = +3.5;
Δ = b2-4ac
Δ = -142-4·2·3.5
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{42}}{2*2}=\frac{14-2\sqrt{42}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{42}}{2*2}=\frac{14+2\sqrt{42}}{4}
$