8.5=6.5(2d-3)d

Solution for 8.5=6.5(2d-3)d equation:

8.5=6.5(2d-3)d

We move all terms to the left:

8.5-(6.5(2d-3)d)=0


We calculate terms in parentheses: -(6.5(2d-3)d), so:

6.5(2d-3)d

We multiply parentheses

12d^2-18d

Back to the equation:

-(12d^2-18d)


We get rid of parentheses

-12d^2+18d+8.5=0

a = -12; b = 18; c = +8.5;
Δ = b2-4ac
Δ = 182-4·(-12)·8.5
Δ = 732
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:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{183}}{2*-12}=\frac{-18-2\sqrt{183}}{-24}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{183}}{2*-12}=\frac{-18+2\sqrt{183}}{-24}
$