8x+2=72/x

Solution for 8x+2=72/x equation:

8x+2=72/x

We move all terms to the left:

8x+2-(72/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+72/x)+2=0

We get rid of parentheses

8x-72/x+2=0

We multiply all the terms by the denominator


8x*x+2*x-72=0

We add all the numbers together, and all the variables

2x+8x*x-72=0

Wy multiply elements

8x^2+2x-72=0

a = 8; b = 2; c = -72;
Δ = b2-4ac
Δ = 22-4·8·(-72)
Δ = 2308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2308}=\sqrt{4*577}=\sqrt{4}*\sqrt{577}=2\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{577}}{2*8}=\frac{-2-2\sqrt{577}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{577}}{2*8}=\frac{-2+2\sqrt{577}}{16}
$