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

We add all the numbers together, and all the variables

232b-5*128b^2=0

Wy multiply elements

-640b^2+232b=0

a = -640; b = 232; c = 0;
Δ = b2-4ac
Δ = 2322-4·(-640)·0
Δ = 53824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{53824}=232$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(232)-232}{2*-640}=\frac{-464}{-1280}
=29/80
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(232)+232}{2*-640}=\frac{0}{-1280}
=0
$