7/8b-4=15/16b+1

Solution for 7/8b-4=15/16b+1 equation:

7/8b-4=15/16b+1

We move all terms to the left:

7/8b-4-(15/16b+1)=0


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R



Domain of the equation: 16b+1)!=0

b∈R


We get rid of parentheses

7/8b-15/16b-1-4=0

We calculate fractions


112b/128b^2+(-120b)/128b^2-1-4=0

We add all the numbers together, and all the variables

112b/128b^2+(-120b)/128b^2-5=0

We multiply all the terms by the denominator


112b+(-120b)-5*128b^2=0

Wy multiply elements

-640b^2+112b+(-120b)=0

We get rid of parentheses

-640b^2+112b-120b=0

We add all the numbers together, and all the variables

-640b^2-8b=0

a = -640; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-640)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-640}=\frac{0}{-1280}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-640}=\frac{16}{-1280}
=-1/80
$