4a+1/a-1=7

Solution for 4a+1/a-1=7 equation:

4a+1/a-1=7

We move all terms to the left:

4a+1/a-1-(7)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

4a+1/a-8=0

We multiply all the terms by the denominator


4a*a-8*a+1=0

We add all the numbers together, and all the variables

-8a+4a*a+1=0

Wy multiply elements

4a^2-8a+1=0

a = 4; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·4·1
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{3}}{2*4}=\frac{8-4\sqrt{3}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{3}}{2*4}=\frac{8+4\sqrt{3}}{8}
$