2-2/7d=-8d

Solution for 2-2/7d=-8d equation:

2-2/7d=-8d

We move all terms to the left:

2-2/7d-(-8d)=0


Domain of the equation: 7d!=0

d!=0/7

d!=0

d∈R


We get rid of parentheses

-2/7d+8d+2=0

We multiply all the terms by the denominator


8d*7d+2*7d-2=0

Wy multiply elements

56d^2+14d-2=0

a = 56; b = 14; c = -2;
Δ = b2-4ac
Δ = 142-4·56·(-2)
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{161}}{2*56}=\frac{-14-2\sqrt{161}}{112}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{161}}{2*56}=\frac{-14+2\sqrt{161}}{112}
$