((24x2)-2)/5=24+4

Solution for ((24x2)-2)/5=24+4 equation:

((24x^2)-2)/5=24+4

We move all terms to the left:

((24x^2)-2)/5-(24+4)=0

We add all the numbers together, and all the variables

(24x^2-2)/5-28=0

We multiply all the terms by the denominator


(24x^2-2)-28*5=0

We add all the numbers together, and all the variables

(24x^2-2)-140=0

We get rid of parentheses

24x^2-2-140=0

We add all the numbers together, and all the variables

24x^2-142=0

a = 24; b = 0; c = -142;
Δ = b2-4ac
Δ = 02-4·24·(-142)
Δ = 13632
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:

$\sqrt{\Delta}=\sqrt{13632}=\sqrt{64*213}=\sqrt{64}*\sqrt{213}=8\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{213}}{2*24}=\frac{0-8\sqrt{213}}{48}
=-\frac{8\sqrt{213}}{48}
=-\frac{\sqrt{213}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{213}}{2*24}=\frac{0+8\sqrt{213}}{48}
=\frac{8\sqrt{213}}{48}
=\frac{\sqrt{213}}{6}
$