10+10x=500/x-30

Solution for 10+10x=500/x-30 equation:

10+10x=500/x-30

We move all terms to the left:

10+10x-(500/x-30)=0


Domain of the equation: x-30)!=0

x∈R


We get rid of parentheses

10x-500/x+30+10=0

We multiply all the terms by the denominator


10x*x+30*x+10*x-500=0

We add all the numbers together, and all the variables

40x+10x*x-500=0

Wy multiply elements

10x^2+40x-500=0

a = 10; b = 40; c = -500;
Δ = b2-4ac
Δ = 402-4·10·(-500)
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-60\sqrt{6}}{2*10}=\frac{-40-60\sqrt{6}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+60\sqrt{6}}{2*10}=\frac{-40+60\sqrt{6}}{20}
$