-1=x-4.2/x-1.3

Solution for -1=x-4.2/x-1.3 equation:

-1=x-4.2/x-1.3

We move all terms to the left:

-1-(x-4.2/x-1.3)=0


Domain of the equation: x-1.3)!=0

x∈R


We get rid of parentheses

-x+4.2/x+1.3-1=0

We multiply all the terms by the denominator


-x*x+(1.3)*x-1*x+4.2=0

We add all the numbers together, and all the variables

-1x-x*x+(1.3)*x+4.2=0

We multiply parentheses

-1x-x*x+1.3x+4.2=0

Wy multiply elements

-1x^2-1x+1.3x+4.2=0

We add all the numbers together, and all the variables

-1x^2+0.3x+4.2=0

a = -1; b = 0.3; c = +4.2;
Δ = b2-4ac
Δ = 0.32-4·(-1)·4.2
Δ = 16.89
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{-(0.3)-\sqrt{16.89}}{2*-1}=\frac{-0.3-\sqrt{16.89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.3)+\sqrt{16.89}}{2*-1}=\frac{-0.3+\sqrt{16.89}}{-2}
$