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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3X^2+X-6X-2)-(2X(X+3))=0


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

2X(X+3)

We multiply parentheses

2X^2+6X

Back to the equation:

-(2X^2+6X)


We get rid of parentheses

3X^2-2X^2+X-6X-6X-2=0

We add all the numbers together, and all the variables

X^2-11X-2=0

a = 1; b = -11; c = -2;
Δ = b2-4ac
Δ = -112-4·1·(-2)
Δ = 129
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{-(-11)-\sqrt{129}}{2*1}=\frac{11-\sqrt{129}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{129}}{2*1}=\frac{11+\sqrt{129}}{2}
$