3d^2-10d=16

Solution for 3d^2-10d=16 equation:

3d^2-10d=16

We move all terms to the left:

3d^2-10d-(16)=0

a = 3; b = -10; c = -16;
Δ = b2-4ac
Δ = -102-4·3·(-16)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{73}}{2*3}=\frac{10-2\sqrt{73}}{6}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{73}}{2*3}=\frac{10+2\sqrt{73}}{6}
$