3/4b-4=-7/8b+1

Solution for 3/4b-4=-7/8b+1 equation:

3/4b-4=-7/8b+1

We move all terms to the left:

3/4b-4-(-7/8b+1)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 8b+1)!=0

b∈R


We get rid of parentheses

3/4b+7/8b-1-4=0

We calculate fractions


24b/32b^2+28b/32b^2-1-4=0

We add all the numbers together, and all the variables

24b/32b^2+28b/32b^2-5=0

We multiply all the terms by the denominator


24b+28b-5*32b^2=0

We add all the numbers together, and all the variables

52b-5*32b^2=0

Wy multiply elements

-160b^2+52b=0

a = -160; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-160)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-160}=\frac{-104}{-320}
=13/40
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-160}=\frac{0}{-320}
=0
$