8/b+1=4/2b-7

Solution for 8/b+1=4/2b-7 equation:

8/b+1=4/2b-7

We move all terms to the left:

8/b+1-(4/2b-7)=0


Domain of the equation: b!=0

b∈R



Domain of the equation: 2b-7)!=0

b∈R


We get rid of parentheses

8/b-4/2b+7+1=0

We calculate fractions


16b/2b^2+(-4b)/2b^2+7+1=0

We add all the numbers together, and all the variables

16b/2b^2+(-4b)/2b^2+8=0

We multiply all the terms by the denominator


16b+(-4b)+8*2b^2=0

Wy multiply elements

16b^2+16b+(-4b)=0

We get rid of parentheses

16b^2+16b-4b=0

We add all the numbers together, and all the variables

16b^2+12b=0

a = 16; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·16·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*16}=\frac{-24}{32}
=-3/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*16}=\frac{0}{32}
=0
$