150=16d^2

Solution for 150=16d^2 equation:

150=16d^2

We move all terms to the left:

150-(16d^2)=0

a = -16; b = 0; c = +150;
Δ = b2-4ac
Δ = 02-4·(-16)·150
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*-16}=\frac{0-40\sqrt{6}}{-32}
=-\frac{40\sqrt{6}}{-32}
=-\frac{5\sqrt{6}}{-4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*-16}=\frac{0+40\sqrt{6}}{-32}
=\frac{40\sqrt{6}}{-32}
=\frac{5\sqrt{6}}{-4}
$