1/5x+8=110x+9.

Solution for 1/5x+8=110x+9. equation:

1/5x+8=110x+9.

We move all terms to the left:

1/5x+8-(110x+9.)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(110x+9)+8=0

We get rid of parentheses

1/5x-110x-9+8=0

We multiply all the terms by the denominator


-110x*5x-9*5x+8*5x+1=0

Wy multiply elements

-550x^2-45x+40x+1=0

We add all the numbers together, and all the variables

-550x^2-5x+1=0

a = -550; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-550)·1
Δ = 2225
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:

$\sqrt{\Delta}=\sqrt{2225}=\sqrt{25*89}=\sqrt{25}*\sqrt{89}=5\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{89}}{2*-550}=\frac{5-5\sqrt{89}}{-1100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{89}}{2*-550}=\frac{5+5\sqrt{89}}{-1100}
$