115(2-x)+1=1/10x

Solution for 115(2-x)+1=1/10x equation:

115(2-x)+1=1/10x

We move all terms to the left:

115(2-x)+1-(1/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

115(-1x+2)-(+1/10x)+1=0

We multiply parentheses

-115x-(+1/10x)+230+1=0

We get rid of parentheses

-115x-1/10x+230+1=0

We multiply all the terms by the denominator


-115x*10x+230*10x+1*10x-1=0

Wy multiply elements

-1150x^2+2300x+10x-1=0

We add all the numbers together, and all the variables

-1150x^2+2310x-1=0

a = -1150; b = 2310; c = -1;
Δ = b2-4ac
Δ = 23102-4·(-1150)·(-1)
Δ = 5331500
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:

$\sqrt{\Delta}=\sqrt{5331500}=\sqrt{100*53315}=\sqrt{100}*\sqrt{53315}=10\sqrt{53315}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2310)-10\sqrt{53315}}{2*-1150}=\frac{-2310-10\sqrt{53315}}{-2300}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2310)+10\sqrt{53315}}{2*-1150}=\frac{-2310+10\sqrt{53315}}{-2300}
$