600x-600(x-10)=3x(x-10)

Solution for 600x-600(x-10)=3x(x-10) equation:

600x-600(x-10)=3x(x-10)

We move all terms to the left:

600x-600(x-10)-(3x(x-10))=0

We multiply parentheses

600x-600x-(3x(x-10))+6000=0


We calculate terms in parentheses: -(3x(x-10)), so:

3x(x-10)

We multiply parentheses

3x^2-30x

Back to the equation:

-(3x^2-30x)


We add all the numbers together, and all the variables

-(3x^2-30x)+6000=0

We get rid of parentheses

-3x^2+30x+6000=0

a = -3; b = 30; c = +6000;
Δ = b2-4ac
Δ = 302-4·(-3)·6000
Δ = 72900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{72900}=270$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-270}{2*-3}=\frac{-300}{-6}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+270}{2*-3}=\frac{240}{-6}
=-40
$