(3a+4)/a=a

Solution for (3a+4)/a=a equation:

(3a+4)/a=a

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

-1a+(3a+4)/a=0

We multiply all the terms by the denominator


-1a*a+(3a+4)=0

Wy multiply elements

-1a^2+(3a+4)=0

We get rid of parentheses

-1a^2+3a+4=0

a = -1; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-1)·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*-1}=\frac{-8}{-2}
=+4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*-1}=\frac{2}{-2}
=-1
$