24x=5(x^2-1)

Solution for 24x=5(x^2-1) equation:

24x=5(x^2-1)

We move all terms to the left:

24x-(5(x^2-1))=0


We calculate terms in parentheses: -(5(x^2-1)), so:

5(x^2-1)

We multiply parentheses

5x^2-5

Back to the equation:

-(5x^2-5)


We get rid of parentheses

-5x^2+24x+5=0

a = -5; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·(-5)·5
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-26}{2*-5}=\frac{-50}{-10}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+26}{2*-5}=\frac{2}{-10}
=-1/5
$