33=(x^2)-(3x)*(2x)*(-6)

Solution for 33=(x^2)-(3x)*(2x)*(-6) equation:

33=(x^2)-(3x)(2x)(-6)

We move all terms to the left:

33-((x^2)-(3x)(2x)(-6))=0


We calculate terms in parentheses: -(x^2-3x2x(-6)), so:

x^2-3x2x(-6)

We multiply parentheses

x^2+18x^2

We add all the numbers together, and all the variables

19x^2

Back to the equation:

-(19x^2)


a = -19; b = 0; c = +33;
Δ = b2-4ac
Δ = 02-4·(-19)·33
Δ = 2508
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:

$\sqrt{\Delta}=\sqrt{2508}=\sqrt{4*627}=\sqrt{4}*\sqrt{627}=2\sqrt{627}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{627}}{2*-19}=\frac{0-2\sqrt{627}}{-38}
=-\frac{2\sqrt{627}}{-38}
=-\frac{\sqrt{627}}{-19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{627}}{2*-19}=\frac{0+2\sqrt{627}}{-38}
=\frac{2\sqrt{627}}{-38}
=\frac{\sqrt{627}}{-19}
$