600=3(x-6)(2.9x-6)

Solution for 600=3(x-6)(2.9x-6) equation:

600=3(x-6)(2.9x-6)

We move all terms to the left:

600-(3(x-6)(2.9x-6))=0

We multiply parentheses ..

-(3(+2x^2-6x-12x+36))+600=0


We calculate terms in parentheses: -(3(+2x^2-6x-12x+36)), so:

3(+2x^2-6x-12x+36)

We multiply parentheses

6x^2-18x-36x+108

We add all the numbers together, and all the variables

6x^2-54x+108

Back to the equation:

-(6x^2-54x+108)


We get rid of parentheses

-6x^2+54x-108+600=0

We add all the numbers together, and all the variables

-6x^2+54x+492=0

a = -6; b = 54; c = +492;
Δ = b2-4ac
Δ = 542-4·(-6)·492
Δ = 14724
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:

$\sqrt{\Delta}=\sqrt{14724}=\sqrt{36*409}=\sqrt{36}*\sqrt{409}=6\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{409}}{2*-6}=\frac{-54-6\sqrt{409}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{409}}{2*-6}=\frac{-54+6\sqrt{409}}{-12}
$