2+d=15-7/8d

Solution for 2+d=15-7/8d equation:

2+d=15-7/8d

We move all terms to the left:

2+d-(15-7/8d)=0


Domain of the equation: 8d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

d-(-7/8d+15)+2=0

We get rid of parentheses

d+7/8d-15+2=0

We multiply all the terms by the denominator


d*8d-15*8d+2*8d+7=0

Wy multiply elements

8d^2-120d+16d+7=0

We add all the numbers together, and all the variables

8d^2-104d+7=0

a = 8; b = -104; c = +7;
Δ = b2-4ac
Δ = -1042-4·8·7
Δ = 10592
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:

$\sqrt{\Delta}=\sqrt{10592}=\sqrt{16*662}=\sqrt{16}*\sqrt{662}=4\sqrt{662}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{662}}{2*8}=\frac{104-4\sqrt{662}}{16}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{662}}{2*8}=\frac{104+4\sqrt{662}}{16}
$