x+30/x+10=120

Solution for x+30/x+10=120 equation:

x+30/x+10=120

We move all terms to the left:

x+30/x+10-(120)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+30/x-110=0

We multiply all the terms by the denominator


x*x-110*x+30=0

We add all the numbers together, and all the variables

-110x+x*x+30=0

Wy multiply elements

x^2-110x+30=0

a = 1; b = -110; c = +30;
Δ = b2-4ac
Δ = -1102-4·1·30
Δ = 11980
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:

$\sqrt{\Delta}=\sqrt{11980}=\sqrt{4*2995}=\sqrt{4}*\sqrt{2995}=2\sqrt{2995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{2995}}{2*1}=\frac{110-2\sqrt{2995}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{2995}}{2*1}=\frac{110+2\sqrt{2995}}{2}
$