4/3b+25=5b-18

Solution for 4/3b+25=5b-18 equation:

4/3b+25=5b-18

We move all terms to the left:

4/3b+25-(5b-18)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We get rid of parentheses

4/3b-5b+18+25=0

We multiply all the terms by the denominator


-5b*3b+18*3b+25*3b+4=0

Wy multiply elements

-15b^2+54b+75b+4=0

We add all the numbers together, and all the variables

-15b^2+129b+4=0

a = -15; b = 129; c = +4;
Δ = b2-4ac
Δ = 1292-4·(-15)·4
Δ = 16881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(129)-\sqrt{16881}}{2*-15}=\frac{-129-\sqrt{16881}}{-30}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(129)+\sqrt{16881}}{2*-15}=\frac{-129+\sqrt{16881}}{-30}
$