5/3a+5/16a=26

Solution for 5/3a+5/16a=26 equation:

5/3a+5/16a=26

We move all terms to the left:

5/3a+5/16a-(26)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 16a!=0

a!=0/16

a!=0

a∈R


We calculate fractions


80a/48a^2+15a/48a^2-26=0

We multiply all the terms by the denominator


80a+15a-26*48a^2=0

We add all the numbers together, and all the variables

95a-26*48a^2=0

Wy multiply elements

-1248a^2+95a=0

a = -1248; b = 95; c = 0;
Δ = b2-4ac
Δ = 952-4·(-1248)·0
Δ = 9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9025}=95$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(95)-95}{2*-1248}=\frac{-190}{-2496}
=95/1248
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(95)+95}{2*-1248}=\frac{0}{-2496}
=0
$