1/b+3b/5b-2=0

Solution for 1/b+3b/5b-2=0 equation:

1/b+3b/5b-2=0


Domain of the equation: b!=0

b∈R



Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We calculate fractions


3b^2/5b^2+5b/5b^2-2=0

We multiply all the terms by the denominator


3b^2+5b-2*5b^2=0

Wy multiply elements

3b^2-10b^2+5b=0

We add all the numbers together, and all the variables

-7b^2+5b=0

a = -7; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-7)·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*-7}=\frac{-10}{-14}
=5/7
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-7}=\frac{0}{-14}
=0
$