(2x-3)x=65

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

(2x-3)x=65

We move all terms to the left:

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

We multiply parentheses

2x^2-3x-65=0

a = 2; b = -3; c = -65;
Δ = b2-4ac
Δ = -32-4·2·(-65)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-23}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+23}{2*2}=\frac{26}{4}
=6+1/2
$