5/3b+7+2/5b=19

Solution for 5/3b+7+2/5b=19 equation:

5/3b+7+2/5b=19

We move all terms to the left:

5/3b+7+2/5b-(19)=0


Domain of the equation: 3b!=0

b!=0/3

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

5/3b+2/5b-12=0

We calculate fractions


25b/15b^2+6b/15b^2-12=0

We multiply all the terms by the denominator


25b+6b-12*15b^2=0

We add all the numbers together, and all the variables

31b-12*15b^2=0

Wy multiply elements

-180b^2+31b=0

a = -180; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-180)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-180}=\frac{-62}{-360}
=31/180
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-180}=\frac{0}{-360}
=0
$