5x^2-24x-3=2

Solution for 5x^2-24x-3=2 equation:

5x^2-24x-3=2

We move all terms to the left:

5x^2-24x-3-(2)=0

We add all the numbers together, and all the variables

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