-8x+40/x=2

Solution for -8x+40/x=2 equation:

-8x+40/x=2

We move all terms to the left:

-8x+40/x-(2)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


-8x*x-2*x+40=0

We add all the numbers together, and all the variables

-2x-8x*x+40=0

Wy multiply elements

-8x^2-2x+40=0

a = -8; b = -2; c = +40;
Δ = b2-4ac
Δ = -22-4·(-8)·40
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{321}}{2*-8}=\frac{2-2\sqrt{321}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{321}}{2*-8}=\frac{2+2\sqrt{321}}{-16}
$