5x+20/(1x-9)=10

Solution for 5x+20/(1x-9)=10 equation:

5x+20/(1x-9)=10

We move all terms to the left:

5x+20/(1x-9)-(10)=0


Domain of the equation: (1x-9)!=0

We move all terms containing x to the left, all other terms to the right

x!=9

x∈R


We add all the numbers together, and all the variables

5x+20/(x-9)-10=0

We multiply all the terms by the denominator


5x*(x-9)-10*(x-9)+20=0

We multiply parentheses

5x^2-45x-10x+90+20=0

We add all the numbers together, and all the variables

5x^2-55x+110=0

a = 5; b = -55; c = +110;
Δ = b2-4ac
Δ = -552-4·5·110
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{33}}{2*5}=\frac{55-5\sqrt{33}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{33}}{2*5}=\frac{55+5\sqrt{33}}{10}
$