2x(3.25x+1)=65

Solution for 2x(3.25x+1)=65 equation:

2x(3.25x+1)=65

We move all terms to the left:

2x(3.25x+1)-(65)=0

We multiply parentheses

6x^2+2x-65=0

a = 6; b = 2; c = -65;
Δ = b2-4ac
Δ = 22-4·6·(-65)
Δ = 1564
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:

$\sqrt{\Delta}=\sqrt{1564}=\sqrt{4*391}=\sqrt{4}*\sqrt{391}=2\sqrt{391}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{391}}{2*6}=\frac{-2-2\sqrt{391}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{391}}{2*6}=\frac{-2+2\sqrt{391}}{12}
$