3x(x-1)=2(x2+27)

Solution for 3x(x-1)=2(x2+27) equation:

3x(x-1)=2(x2+27)

We move all terms to the left:

3x(x-1)-(2(x2+27))=0

We add all the numbers together, and all the variables

-(2(+x^2+27))+3x(x-1)=0

We multiply parentheses

-(2(+x^2+27))+3x^2-3x=0


We calculate terms in parentheses: -(2(+x^2+27)), so:

2(+x^2+27)

We multiply parentheses

2x^2+54

Back to the equation:

-(2x^2+54)


We add all the numbers together, and all the variables

3x^2-3x-(2x^2+54)=0

We get rid of parentheses

3x^2-2x^2-3x-54=0

We add all the numbers together, and all the variables

x^2-3x-54=0

a = 1; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·1·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*1}=\frac{18}{2}
=9
$