-3/4b+7+2/b=19

Solution for -3/4b+7+2/b=19 equation:

-3/4b+7+2/b=19

We move all terms to the left:

-3/4b+7+2/b-(19)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

-3/4b+2/b-12=0

We calculate fractions


(-3b)/4b^2+8b/4b^2-12=0

We multiply all the terms by the denominator


(-3b)+8b-12*4b^2=0

We add all the numbers together, and all the variables

8b+(-3b)-12*4b^2=0

Wy multiply elements

-48b^2+8b+(-3b)=0

We get rid of parentheses

-48b^2+8b-3b=0

We add all the numbers together, and all the variables

-48b^2+5b=0

a = -48; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-48)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-48}=\frac{-10}{-96}
=5/48
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-48}=\frac{0}{-96}
=0
$