1/10x+14.9=-6+2x

Solution for 1/10x+14.9=-6+2x equation:

1/10x+14.9=-6+2x

We move all terms to the left:

1/10x+14.9-(-6+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-6)+14.9=0

We get rid of parentheses

1/10x-2x+6+14.9=0

We multiply all the terms by the denominator


-2x*10x+6*10x+(14.9)*10x+1=0

We multiply parentheses

-2x*10x+6*10x+149x+1=0

Wy multiply elements

-20x^2+60x+149x+1=0

We add all the numbers together, and all the variables

-20x^2+209x+1=0

a = -20; b = 209; c = +1;
Δ = b2-4ac
Δ = 2092-4·(-20)·1
Δ = 43761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(209)-\sqrt{43761}}{2*-20}=\frac{-209-\sqrt{43761}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(209)+\sqrt{43761}}{2*-20}=\frac{-209+\sqrt{43761}}{-40}
$