2a+15/2a=19

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

2a+15/2a=19

We move all terms to the left:

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

Wy multiply elements

4a^2-38a+15=0

a = 4; b = -38; c = +15;
Δ = b2-4ac
Δ = -382-4·4·15
Δ = 1204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{301}}{2*4}=\frac{38-2\sqrt{301}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{301}}{2*4}=\frac{38+2\sqrt{301}}{8}
$