3(2d-8)=11d-18d(d-3)

Solution for 3(2d-8)=11d-18d(d-3) equation:

3(2d-8)=11d-18d(d-3)

We move all terms to the left:

3(2d-8)-(11d-18d(d-3))=0

We multiply parentheses

6d-(11d-18d(d-3))-24=0


We calculate terms in parentheses: -(11d-18d(d-3)), so:

11d-18d(d-3)

We multiply parentheses

-18d^2+11d+54d

We add all the numbers together, and all the variables

-18d^2+65d

Back to the equation:

-(-18d^2+65d)


We get rid of parentheses

18d^2-65d+6d-24=0

We add all the numbers together, and all the variables

18d^2-59d-24=0

a = 18; b = -59; c = -24;
Δ = b2-4ac
Δ = -592-4·18·(-24)
Δ = 5209
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{-(-59)-\sqrt{5209}}{2*18}=\frac{59-\sqrt{5209}}{36}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{5209}}{2*18}=\frac{59+\sqrt{5209}}{36}
$