3x+10/x+10=100

Solution for 3x+10/x+10=100 equation:

3x+10/x+10=100

We move all terms to the left:

3x+10/x+10-(100)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+10/x-90=0

We multiply all the terms by the denominator


3x*x-90*x+10=0

We add all the numbers together, and all the variables

-90x+3x*x+10=0

Wy multiply elements

3x^2-90x+10=0

a = 3; b = -90; c = +10;
Δ = b2-4ac
Δ = -902-4·3·10
Δ = 7980
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:

$\sqrt{\Delta}=\sqrt{7980}=\sqrt{4*1995}=\sqrt{4}*\sqrt{1995}=2\sqrt{1995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1995}}{2*3}=\frac{90-2\sqrt{1995}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1995}}{2*3}=\frac{90+2\sqrt{1995}}{6}
$