6d-24=11d(-18d+54)

Solution for 6d-24=11d(-18d+54) equation:

6d-24=11d(-18d+54)

We move all terms to the left:

6d-24-(11d(-18d+54))=0


We calculate terms in parentheses: -(11d(-18d+54)), so:

11d(-18d+54)

We multiply parentheses

-198d^2+594d

Back to the equation:

-(-198d^2+594d)


We get rid of parentheses

198d^2-594d+6d-24=0

We add all the numbers together, and all the variables

198d^2-588d-24=0

a = 198; b = -588; c = -24;
Δ = b2-4ac
Δ = -5882-4·198·(-24)
Δ = 364752
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:

$\sqrt{\Delta}=\sqrt{364752}=\sqrt{144*2533}=\sqrt{144}*\sqrt{2533}=12\sqrt{2533}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-588)-12\sqrt{2533}}{2*198}=\frac{588-12\sqrt{2533}}{396}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-588)+12\sqrt{2533}}{2*198}=\frac{588+12\sqrt{2533}}{396}
$