3x-5x(x-1)=3

Solution for 3x-5x(x-1)=3 equation:

3x-5x(x-1)=3

We move all terms to the left:

3x-5x(x-1)-(3)=0

We multiply parentheses

-5x^2+3x+5x-3=0

We add all the numbers together, and all the variables

-5x^2+8x-3=0

a = -5; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·(-5)·(-3)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2}{2*-5}=\frac{-6}{-10}
=3/5
$