5a-16/a=4

Solution for 5a-16/a=4 equation:

5a-16/a=4

We move all terms to the left:

5a-16/a-(4)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


5a*a-4*a-16=0

We add all the numbers together, and all the variables

-4a+5a*a-16=0

Wy multiply elements

5a^2-4a-16=0

a = 5; b = -4; c = -16;
Δ = b2-4ac
Δ = -42-4·5·(-16)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{21}}{2*5}=\frac{4-4\sqrt{21}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{21}}{2*5}=\frac{4+4\sqrt{21}}{10}
$