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

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

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

We move all terms to the left:

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


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We add all the numbers together, and all the variables

1/4b+1/5b-12=0

We calculate fractions


5b/20b^2+4b/20b^2-12=0

We multiply all the terms by the denominator


5b+4b-12*20b^2=0

We add all the numbers together, and all the variables

9b-12*20b^2=0

Wy multiply elements

-240b^2+9b=0

a = -240; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-240)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-240}=\frac{-18}{-480}
=3/80
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-240}=\frac{0}{-480}
=0
$