-3x^2-21=24x

Solution for -3x^2-21=24x equation:

-3x^2-21=24x

We move all terms to the left:

-3x^2-21-(24x)=0

a = -3; b = -24; c = -21;
Δ = b2-4ac
Δ = -242-4·(-3)·(-21)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18}{2*-3}=\frac{6}{-6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18}{2*-3}=\frac{42}{-6}
=-7
$