1000/x=-5+0.1x

Solution for 1000/x=-5+0.1x equation:

1000/x=-5+0.1x

We move all terms to the left:

1000/x-(-5+0.1x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1000/x-(0.1x-5)=0

We get rid of parentheses

1000/x-0.1x+5=0

We multiply all the terms by the denominator


-(0.1x)*x+5*x+1000=0

We add all the numbers together, and all the variables

-(+0.1x)*x+5*x+1000=0

We add all the numbers together, and all the variables

5x-(+0.1x)*x+1000=0

We multiply parentheses

-0x^2+5x+1000=0

We add all the numbers together, and all the variables

-1x^2+5x+1000=0

a = -1; b = 5; c = +1000;
Δ = b2-4ac
Δ = 52-4·(-1)·1000
Δ = 4025
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:

$\sqrt{\Delta}=\sqrt{4025}=\sqrt{25*161}=\sqrt{25}*\sqrt{161}=5\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{161}}{2*-1}=\frac{-5-5\sqrt{161}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{161}}{2*-1}=\frac{-5+5\sqrt{161}}{-2}
$