d^2-28d=-9

Solution for d^2-28d=-9 equation:

d^2-28d=-9

We move all terms to the left:

d^2-28d-(-9)=0

We add all the numbers together, and all the variables

d^2-28d+9=0

a = 1; b = -28; c = +9;
Δ = b2-4ac
Δ = -282-4·1·9
Δ = 748
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:

$\sqrt{\Delta}=\sqrt{748}=\sqrt{4*187}=\sqrt{4}*\sqrt{187}=2\sqrt{187}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{187}}{2*1}=\frac{28-2\sqrt{187}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{187}}{2*1}=\frac{28+2\sqrt{187}}{2}
$