D=5(4x+1)-2x(4x+1)

Solution for D=5(4x+1)-2x(4x+1) equation:

=5(4D+1)-2D(4D+1)

We move all terms to the left:

-(5(4D+1)-2D(4D+1))=0


We calculate terms in parentheses: -(5(4D+1)-2D(4D+1)), so:

5(4D+1)-2D(4D+1)

We multiply parentheses

-8D^2+20D-2D+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-5=0

a = 8; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·8·(-5)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-22}{2*8}=\frac{-4}{16}
=-1/4
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+22}{2*8}=\frac{40}{16}
=2+1/2
$