21-24x=3x2

Solution for 21-24x=3x2 equation:

21-24x=3x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-3x^2-24x+21=0

a = -3; b = -24; c = +21;
Δ = b2-4ac
Δ = -242-4·(-3)·21
Δ = 828
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{23}}{2*-3}=\frac{24-6\sqrt{23}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{23}}{2*-3}=\frac{24+6\sqrt{23}}{-6}
$