(-10x+65)x=2

Solution for (-10x+65)x=2 equation:

(-10x+65)x=2

We move all terms to the left:

(-10x+65)x-(2)=0

We multiply parentheses

-10x^2+65x-2=0

a = -10; b = 65; c = -2;
Δ = b2-4ac
Δ = 652-4·(-10)·(-2)
Δ = 4145
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{-(65)-\sqrt{4145}}{2*-10}=\frac{-65-\sqrt{4145}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4145}}{2*-10}=\frac{-65+\sqrt{4145}}{-20}
$