48=23d+2.0d^2

Solution for 48=23d+2.0d^2 equation:

48=23d+2.0d^2

We move all terms to the left:

48-(23d+2.0d^2)=0

We get rid of parentheses

-2.0d^2-23d+48=0

We add all the numbers together, and all the variables

-2d^2-23d+48=0

a = -2; b = -23; c = +48;
Δ = b2-4ac
Δ = -232-4·(-2)·48
Δ = 913
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{-(-23)-\sqrt{913}}{2*-2}=\frac{23-\sqrt{913}}{-4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{913}}{2*-2}=\frac{23+\sqrt{913}}{-4}
$