9(8d-5)+13=12d2

Solution for 9(8d-5)+13=12d2 equation:

9(8d-5)+13=12d^2

We move all terms to the left:

9(8d-5)+13-(12d^2)=0

determiningTheFunctionDomain
-12d^2+9(8d-5)+13=0

We multiply parentheses

-12d^2+72d-45+13=0

We add all the numbers together, and all the variables

-12d^2+72d-32=0

a = -12; b = 72; c = -32;
Δ = b2-4ac
Δ = 722-4·(-12)·(-32)
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-8\sqrt{57}}{2*-12}=\frac{-72-8\sqrt{57}}{-24}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+8\sqrt{57}}{2*-12}=\frac{-72+8\sqrt{57}}{-24}
$