(3x-2)x=260

Solution for (3x-2)x=260 equation:

(3x-2)x=260

We move all terms to the left:

(3x-2)x-(260)=0

We multiply parentheses

3x^2-2x-260=0

a = 3; b = -2; c = -260;
Δ = b2-4ac
Δ = -22-4·3·(-260)
Δ = 3124
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:

$\sqrt{\Delta}=\sqrt{3124}=\sqrt{4*781}=\sqrt{4}*\sqrt{781}=2\sqrt{781}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{781}}{2*3}=\frac{2-2\sqrt{781}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{781}}{2*3}=\frac{2+2\sqrt{781}}{6}
$