0.15x+5/7x+19=x

Solution for 0.15x+5/7x+19=x equation:

0.15x+5/7x+19=x

We move all terms to the left:

0.15x+5/7x+19-(x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-0.85x+5/7x+19=0

We multiply all the terms by the denominator


-(0.85x)*7x+19*7x+5=0

We add all the numbers together, and all the variables

-(+0.85x)*7x+19*7x+5=0

We multiply parentheses

-0x^2+19*7x+5=0

Wy multiply elements

-0x^2+133x+5=0

We add all the numbers together, and all the variables

-1x^2+133x+5=0

a = -1; b = 133; c = +5;
Δ = b2-4ac
Δ = 1332-4·(-1)·5
Δ = 17709
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{-(133)-\sqrt{17709}}{2*-1}=\frac{-133-\sqrt{17709}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(133)+\sqrt{17709}}{2*-1}=\frac{-133+\sqrt{17709}}{-2}
$