24-x=2x^2

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

24-x=2x^2

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

-2x^2-1x+24=0

a = -2; b = -1; c = +24;
Δ = b2-4ac
Δ = -12-4·(-2)·24
Δ = 193
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{-(-1)-\sqrt{193}}{2*-2}=\frac{1-\sqrt{193}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{193}}{2*-2}=\frac{1+\sqrt{193}}{-4}
$