2a+15a/2a=19

Solution for 2a+15a/2a=19 equation:

2a+15a/2a=19

We move all terms to the left:

2a+15a/2a-(19)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


2a*2a+15a-19*2a=0

We add all the numbers together, and all the variables

15a+2a*2a-19*2a=0

Wy multiply elements

4a^2+15a-38a=0

We add all the numbers together, and all the variables

4a^2-23a=0

a = 4; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·4·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*4}=\frac{0}{8}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*4}=\frac{46}{8}
=5+3/4
$