2/3a+1/5a=90

Solution for 2/3a+1/5a=90 equation:

2/3a+1/5a=90

We move all terms to the left:

2/3a+1/5a-(90)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We calculate fractions


10a/15a^2+3a/15a^2-90=0

We multiply all the terms by the denominator


10a+3a-90*15a^2=0

We add all the numbers together, and all the variables

13a-90*15a^2=0

Wy multiply elements

-1350a^2+13a=0

a = -1350; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-1350)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-1350}=\frac{-26}{-2700}
=13/1350
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-1350}=\frac{0}{-2700}
=0
$