6(d-8)=3(14-d)d=

Solution for 6(d-8)=3(14-d)d= equation:

6(d-8)=3(14-d)d=

We move all terms to the left:

6(d-8)-(3(14-d)d)=0

We add all the numbers together, and all the variables

6(d-8)-(3(-1d+14)d)=0

We multiply parentheses

6d-(3(-1d+14)d)-48=0


We calculate terms in parentheses: -(3(-1d+14)d), so:

3(-1d+14)d

We multiply parentheses

-3d^2+42d

Back to the equation:

-(-3d^2+42d)


We get rid of parentheses

3d^2-42d+6d-48=0

We add all the numbers together, and all the variables

3d^2-36d-48=0

a = 3; b = -36; c = -48;
Δ = b2-4ac
Δ = -362-4·3·(-48)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{13}}{2*3}=\frac{36-12\sqrt{13}}{6}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{13}}{2*3}=\frac{36+12\sqrt{13}}{6}
$