220d^2-88d=22(10d+4)

Solution for 220d^2-88d=22(10d+4) equation:

220d^2-88d=22(10d+4)

We move all terms to the left:

220d^2-88d-(22(10d+4))=0


We calculate terms in parentheses: -(22(10d+4)), so:

22(10d+4)

We multiply parentheses

220d+88

Back to the equation:

-(220d+88)


We get rid of parentheses

220d^2-88d-220d-88=0

We add all the numbers together, and all the variables

220d^2-308d-88=0

a = 220; b = -308; c = -88;
Δ = b2-4ac
Δ = -3082-4·220·(-88)
Δ = 172304
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:

$\sqrt{\Delta}=\sqrt{172304}=\sqrt{1936*89}=\sqrt{1936}*\sqrt{89}=44\sqrt{89}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-308)-44\sqrt{89}}{2*220}=\frac{308-44\sqrt{89}}{440}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-308)+44\sqrt{89}}{2*220}=\frac{308+44\sqrt{89}}{440}
$