5x-24/x-4=3

Solution for 5x-24/x-4=3 equation:

5x-24/x-4=3

We move all terms to the left:

5x-24/x-4-(3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-24/x-7=0

We multiply all the terms by the denominator


5x*x-7*x-24=0

We add all the numbers together, and all the variables

-7x+5x*x-24=0

Wy multiply elements

5x^2-7x-24=0

a = 5; b = -7; c = -24;
Δ = b2-4ac
Δ = -72-4·5·(-24)
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{-(-7)-23}{2*5}=\frac{-16}{10}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*5}=\frac{30}{10}
=3
$