(x)=x(75-3x)

Solution for (x)=x(75-3x) equation:

(x)=x(75-3x)

We move all terms to the left:

(x)-(x(75-3x))=0

We add all the numbers together, and all the variables

x-(x(-3x+75))=0


We calculate terms in parentheses: -(x(-3x+75)), so:

x(-3x+75)

We multiply parentheses

-3x^2+75x

Back to the equation:

-(-3x^2+75x)


We get rid of parentheses

3x^2-75x+x=0

We add all the numbers together, and all the variables

3x^2-74x=0

a = 3; b = -74; c = 0;
Δ = b2-4ac
Δ = -742-4·3·0
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-74}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+74}{2*3}=\frac{148}{6}
=24+2/3
$