B/x-5=-4x

Solution for B/x-5=-4x equation:

/B-5=-4B

We move all terms to the left:

/B-5-(-4B)=0


Domain of the equation: B!=0

B∈R


We get rid of parentheses

/B+4B-5=0

We multiply all the terms by the denominator


4B*B-5*B+=0

We add all the numbers together, and all the variables

-5B+4B*B=0

Wy multiply elements

4B^2-5B=0

a = 4; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·4·0
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*4}=\frac{0}{8}
=0
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*4}=\frac{10}{8}
=1+1/4
$