1/4b-3=1/5b+15

Solution for 1/4b-3=1/5b+15 equation:

1/4b-3=1/5b+15

We move all terms to the left:

1/4b-3-(1/5b+15)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 5b+15)!=0

b∈R


We get rid of parentheses

1/4b-1/5b-15-3=0

We calculate fractions


5b/20b^2+(-4b)/20b^2-15-3=0

We add all the numbers together, and all the variables

5b/20b^2+(-4b)/20b^2-18=0

We multiply all the terms by the denominator


5b+(-4b)-18*20b^2=0

Wy multiply elements

-360b^2+5b+(-4b)=0

We get rid of parentheses

-360b^2+5b-4b=0

We add all the numbers together, and all the variables

-360b^2+b=0

a = -360; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-360)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-360}=\frac{-2}{-720}
=1/360
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-360}=\frac{0}{-720}
=0
$