2/3b+4/5b=90

Solution for 2/3b+4/5b=90 equation:

2/3b+4/5b=90

We move all terms to the left:

2/3b+4/5b-(90)=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 calculate fractions


10b/15b^2+12b/15b^2-90=0

We multiply all the terms by the denominator


10b+12b-90*15b^2=0

We add all the numbers together, and all the variables

22b-90*15b^2=0

Wy multiply elements

-1350b^2+22b=0

a = -1350; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-1350)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-1350}=\frac{-44}{-2700}
=11/675
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-1350}=\frac{0}{-2700}
=0
$