5/2d+8=7/8d-8

Solution for 5/2d+8=7/8d-8 equation:

5/2d+8=7/8d-8

We move all terms to the left:

5/2d+8-(7/8d-8)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 8d-8)!=0

d∈R


We get rid of parentheses

5/2d-7/8d+8+8=0

We calculate fractions


40d/16d^2+(-14d)/16d^2+8+8=0

We add all the numbers together, and all the variables

40d/16d^2+(-14d)/16d^2+16=0

We multiply all the terms by the denominator


40d+(-14d)+16*16d^2=0

Wy multiply elements

256d^2+40d+(-14d)=0

We get rid of parentheses

256d^2+40d-14d=0

We add all the numbers together, and all the variables

256d^2+26d=0

a = 256; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·256·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*256}=\frac{-52}{512}
=-13/128
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*256}=\frac{0}{512}
=0
$