65=x(3x-2)

Solution for 65=x(3x-2) equation:

65=x(3x-2)

We move all terms to the left:

65-(x(3x-2))=0


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

x(3x-2)

We multiply parentheses

3x^2-2x

Back to the equation:

-(3x^2-2x)


We get rid of parentheses

-3x^2+2x+65=0

a = -3; b = 2; c = +65;
Δ = b2-4ac
Δ = 22-4·(-3)·65
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-28}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+28}{2*-3}=\frac{26}{-6}
=-4+1/3
$