-5x+50/x=5

Solution for -5x+50/x=5 equation:

-5x+50/x=5

We move all terms to the left:

-5x+50/x-(5)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


-5x*x-5*x+50=0

We add all the numbers together, and all the variables

-5x-5x*x+50=0

Wy multiply elements

-5x^2-5x+50=0

a = -5; b = -5; c = +50;
Δ = b2-4ac
Δ = -52-4·(-5)·50
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{41}}{2*-5}=\frac{5-5\sqrt{41}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{41}}{2*-5}=\frac{5+5\sqrt{41}}{-10}
$