1/10x+110=8-2x

Solution for 1/10x+110=8-2x equation:

1/10x+110=8-2x

We move all terms to the left:

1/10x+110-(8-2x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

1/10x-(-2x+8)+110=0

We get rid of parentheses

1/10x+2x-8+110=0

We multiply all the terms by the denominator


2x*10x-8*10x+110*10x+1=0

Wy multiply elements

20x^2-80x+1100x+1=0

We add all the numbers together, and all the variables

20x^2+1020x+1=0

a = 20; b = 1020; c = +1;
Δ = b2-4ac
Δ = 10202-4·20·1
Δ = 1040320
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:

$\sqrt{\Delta}=\sqrt{1040320}=\sqrt{64*16255}=\sqrt{64}*\sqrt{16255}=8\sqrt{16255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1020)-8\sqrt{16255}}{2*20}=\frac{-1020-8\sqrt{16255}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1020)+8\sqrt{16255}}{2*20}=\frac{-1020+8\sqrt{16255}}{40}
$