24x-11/x=-25

Solution for 24x-11/x=-25 equation:

24x-11/x=-25

We move all terms to the left:

24x-11/x-(-25)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

24x-11/x+25=0

We multiply all the terms by the denominator


24x*x+25*x-11=0

We add all the numbers together, and all the variables

25x+24x*x-11=0

Wy multiply elements

24x^2+25x-11=0

a = 24; b = 25; c = -11;
Δ = b2-4ac
Δ = 252-4·24·(-11)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-41}{2*24}=\frac{-66}{48}
=-1+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+41}{2*24}=\frac{16}{48}
=1/3
$