4.6d=54-d^2

Solution for 4.6d=54-d^2 equation:

4.6d=54-d^2

We move all terms to the left:

4.6d-(54-d^2)=0

We get rid of parentheses

d^2+4.6d-54=0

a = 1; b = 4.6; c = -54;
Δ = b2-4ac
Δ = 4.62-4·1·(-54)
Δ = 237.16
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{-(4.6)-\sqrt{237.16}}{2*1}=\frac{-4.6-\sqrt{237.16}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.6)+\sqrt{237.16}}{2*1}=\frac{-4.6+\sqrt{237.16}}{2}
$