x=5(x+5)(6-x)

Solution for x=5(x+5)(6-x) equation:

x=5(x+5)(6-x)

We move all terms to the left:

x-(5(x+5)(6-x))=0

We add all the numbers together, and all the variables

x-(5(x+5)(-1x+6))=0

We multiply parentheses ..

-(5(-1x^2+6x-5x+30))+x=0


We calculate terms in parentheses: -(5(-1x^2+6x-5x+30)), so:

5(-1x^2+6x-5x+30)

We multiply parentheses

-5x^2+30x-25x+150

We add all the numbers together, and all the variables

-5x^2+5x+150

Back to the equation:

-(-5x^2+5x+150)


We get rid of parentheses

5x^2-5x+x-150=0

We add all the numbers together, and all the variables

5x^2-4x-150=0

a = 5; b = -4; c = -150;
Δ = b2-4ac
Δ = -42-4·5·(-150)
Δ = 3016
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:

$\sqrt{\Delta}=\sqrt{3016}=\sqrt{4*754}=\sqrt{4}*\sqrt{754}=2\sqrt{754}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{754}}{2*5}=\frac{4-2\sqrt{754}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{754}}{2*5}=\frac{4+2\sqrt{754}}{10}
$