4(3^2)-21=3x^2-4x

Solution for 4(3^2)-21=3x^2-4x equation:

4(3^2)-21=3x^2-4x

We move all terms to the left:

4(3^2)-21-(3x^2-4x)=0

We add all the numbers together, and all the variables

-(3x^2-4x)+1828=0

We get rid of parentheses

-3x^2+4x+1828=0

a = -3; b = 4; c = +1828;
Δ = b2-4ac
Δ = 42-4·(-3)·1828
Δ = 21952
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:

$\sqrt{\Delta}=\sqrt{21952}=\sqrt{3136*7}=\sqrt{3136}*\sqrt{7}=56\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-56\sqrt{7}}{2*-3}=\frac{-4-56\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+56\sqrt{7}}{2*-3}=\frac{-4+56\sqrt{7}}{-6}
$