10x+10=200/x

Solution for 10x+10=200/x equation:

10x+10=200/x

We move all terms to the left:

10x+10-(200/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

10x-(+200/x)+10=0

We get rid of parentheses

10x-200/x+10=0

We multiply all the terms by the denominator


10x*x+10*x-200=0

We add all the numbers together, and all the variables

10x+10x*x-200=0

Wy multiply elements

10x^2+10x-200=0

a = 10; b = 10; c = -200;
Δ = b2-4ac
Δ = 102-4·10·(-200)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-90}{2*10}=\frac{-100}{20}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+90}{2*10}=\frac{80}{20}
=4
$