24x-40/9x-5=3

Solution for 24x-40/9x-5=3 equation:

24x-40/9x-5=3

We move all terms to the left:

24x-40/9x-5-(3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

24x-40/9x-8=0

We multiply all the terms by the denominator


24x*9x-8*9x-40=0

Wy multiply elements

216x^2-72x-40=0

a = 216; b = -72; c = -40;
Δ = b2-4ac
Δ = -722-4·216·(-40)
Δ = 39744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{39744}=\sqrt{576*69}=\sqrt{576}*\sqrt{69}=24\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24\sqrt{69}}{2*216}=\frac{72-24\sqrt{69}}{432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24\sqrt{69}}{2*216}=\frac{72+24\sqrt{69}}{432}
$