56/x-2=x-3

Solution for 56/x-2=x-3 equation:

56/x-2=x-3

We move all terms to the left:

56/x-2-(x-3)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

56/x-x+3-2=0

We multiply all the terms by the denominator


-x*x+3*x-2*x+56=0

We add all the numbers together, and all the variables

x-x*x+56=0

Wy multiply elements

-1x^2+x+56=0

a = -1; b = 1; c = +56;
Δ = b2-4ac
Δ = 12-4·(-1)·56
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*-1}=\frac{14}{-2}
=-7
$