4*x*x-(24*x)+33=0

Solution for 4*x*x-(24*x)+33=0 equation:

4x*x-(24x)+33=0

We add all the numbers together, and all the variables

-24x+4x*x+33=0

Wy multiply elements

4x^2-24x+33=0

a = 4; b = -24; c = +33;
Δ = b2-4ac
Δ = -242-4·4·33
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{3}}{2*4}=\frac{24-4\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{3}}{2*4}=\frac{24+4\sqrt{3}}{8}
$