2x-5=21/x-24

Solution for 2x-5=21/x-24 equation:

2x-5=21/x-24

We move all terms to the left:

2x-5-(21/x-24)=0


Domain of the equation: x-24)!=0

x∈R


We get rid of parentheses

2x-21/x+24-5=0

We multiply all the terms by the denominator


2x*x+24*x-5*x-21=0

We add all the numbers together, and all the variables

19x+2x*x-21=0

Wy multiply elements

2x^2+19x-21=0

a = 2; b = 19; c = -21;
Δ = b2-4ac
Δ = 192-4·2·(-21)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-23}{2*2}=\frac{-42}{4}
=-10+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+23}{2*2}=\frac{4}{4}
=1
$