2/3b+5=-1/5b-4

Solution for 2/3b+5=-1/5b-4 equation:

2/3b+5=-1/5b-4

We move all terms to the left:

2/3b+5-(-1/5b-4)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 5b-4)!=0

b∈R


We get rid of parentheses

2/3b+1/5b+4+5=0

We calculate fractions


10b/15b^2+3b/15b^2+4+5=0

We add all the numbers together, and all the variables

10b/15b^2+3b/15b^2+9=0

We multiply all the terms by the denominator


10b+3b+9*15b^2=0

We add all the numbers together, and all the variables

13b+9*15b^2=0

Wy multiply elements

135b^2+13b=0

a = 135; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·135·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*135}=\frac{-26}{270}
=-13/135
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*135}=\frac{0}{270}
=0
$