A=x-54/x-15

Solution for A=x-54/x-15 equation:

=A-54/A-15

We move all terms to the left:

-(A-54/A-15)=0


Domain of the equation: A-15)!=0

A∈R


We get rid of parentheses

-A+54/A+15=0

We multiply all the terms by the denominator


-A*A+15*A+54=0

We add all the numbers together, and all the variables

15A-A*A+54=0

Wy multiply elements

-1A^2+15A+54=0

a = -1; b = 15; c = +54;
Δ = b2-4ac
Δ = 152-4·(-1)·54
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*-1}=\frac{-36}{-2}
=+18
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*-1}=\frac{6}{-2}
=-3
$