3a-5/a=4

Solution for 3a-5/a=4 equation:

3a-5/a=4

We move all terms to the left:

3a-5/a-(4)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


3a*a-4*a-5=0

We add all the numbers together, and all the variables

-4a+3a*a-5=0

Wy multiply elements

3a^2-4a-5=0

a = 3; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·3·(-5)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{19}}{2*3}=\frac{4-2\sqrt{19}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{19}}{2*3}=\frac{4+2\sqrt{19}}{6}
$