(x)=2x2-8x-24

Solution for (x)=2x2-8x-24 equation:

(x)=2x^2-8x-24

We move all terms to the left:

(x)-(2x^2-8x-24)=0

We get rid of parentheses

-2x^2+x+8x+24=0

We add all the numbers together, and all the variables

-2x^2+9x+24=0

a = -2; b = 9; c = +24;
Δ = b2-4ac
Δ = 92-4·(-2)·24
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{273}}{2*-2}=\frac{-9-\sqrt{273}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{273}}{2*-2}=\frac{-9+\sqrt{273}}{-4}
$