3d+16=-2(5-3d)d

Solution for 3d+16=-2(5-3d)d equation:

3d+16=-2(5-3d)d

We move all terms to the left:

3d+16-(-2(5-3d)d)=0

We add all the numbers together, and all the variables

3d-(-2(-3d+5)d)+16=0


We calculate terms in parentheses: -(-2(-3d+5)d), so:

-2(-3d+5)d

We multiply parentheses

6d^2-10d

Back to the equation:

-(6d^2-10d)


We get rid of parentheses

-6d^2+3d+10d+16=0

We add all the numbers together, and all the variables

-6d^2+13d+16=0

a = -6; b = 13; c = +16;
Δ = b2-4ac
Δ = 132-4·(-6)·16
Δ = 553
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{-(13)-\sqrt{553}}{2*-6}=\frac{-13-\sqrt{553}}{-12}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{553}}{2*-6}=\frac{-13+\sqrt{553}}{-12}
$