x+10/x+100=60

Solution for x+10/x+100=60 equation:

x+10/x+100=60

We move all terms to the left:

x+10/x+100-(60)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+10/x+40=0

We multiply all the terms by the denominator


x*x+40*x+10=0

We add all the numbers together, and all the variables

40x+x*x+10=0

Wy multiply elements

x^2+40x+10=0

a = 1; b = 40; c = +10;
Δ = b2-4ac
Δ = 402-4·1·10
Δ = 1560
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:

$\sqrt{\Delta}=\sqrt{1560}=\sqrt{4*390}=\sqrt{4}*\sqrt{390}=2\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{390}}{2*1}=\frac{-40-2\sqrt{390}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{390}}{2*1}=\frac{-40+2\sqrt{390}}{2}
$