x(x-3)-3x=(x+2)3+1

Solution for x(x-3)-3x=(x+2)3+1 equation:

x(x-3)-3x=(x+2)3+1

We move all terms to the left:

x(x-3)-3x-((x+2)3+1)=0

We add all the numbers together, and all the variables

-3x+x(x-3)-((x+2)3+1)=0

We multiply parentheses

x^2-3x-3x-((x+2)3+1)=0


We calculate terms in parentheses: -((x+2)3+1), so:

(x+2)3+1

We multiply parentheses

3x+6+1

We add all the numbers together, and all the variables

3x+7

Back to the equation:

-(3x+7)


We add all the numbers together, and all the variables

x^2-6x-(3x+7)=0

We get rid of parentheses

x^2-6x-3x-7=0

We add all the numbers together, and all the variables

x^2-9x-7=0

a = 1; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·1·(-7)
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{109}}{2*1}=\frac{9-\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{109}}{2*1}=\frac{9+\sqrt{109}}{2}
$