3x-5x(x-2)=3

Solution for 3x-5x(x-2)=3 equation:

3x-5x(x-2)=3

We move all terms to the left:

3x-5x(x-2)-(3)=0

We multiply parentheses

-5x^2+3x+10x-3=0

We add all the numbers together, and all the variables

-5x^2+13x-3=0

a = -5; b = 13; c = -3;
Δ = b2-4ac
Δ = 132-4·(-5)·(-3)
Δ = 109
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{-(13)-\sqrt{109}}{2*-5}=\frac{-13-\sqrt{109}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{109}}{2*-5}=\frac{-13+\sqrt{109}}{-10}
$