11-6d=-8d(d-2)+2d-5

Solution for 11-6d=-8d(d-2)+2d-5 equation:

11-6d=-8d(d-2)+2d-5

We move all terms to the left:

11-6d-(-8d(d-2)+2d-5)=0


We calculate terms in parentheses: -(-8d(d-2)+2d-5), so:

-8d(d-2)+2d-5

We add all the numbers together, and all the variables

2d-8d(d-2)-5

We multiply parentheses

-8d^2+2d+16d-5

We add all the numbers together, and all the variables

-8d^2+18d-5

Back to the equation:

-(-8d^2+18d-5)


We get rid of parentheses

8d^2-18d-6d+5+11=0

We add all the numbers together, and all the variables

8d^2-24d+16=0

a = 8; b = -24; c = +16;
Δ = b2-4ac
Δ = -242-4·8·16
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8}{2*8}=\frac{16}{16}
=1
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8}{2*8}=\frac{32}{16}
=2
$