5(x-1)x=3

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

5(x-1)x=3

We move all terms to the left:

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

We multiply parentheses

5x^2-5x-3=0

a = 5; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·5·(-3)
Δ = 85
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{-(-5)-\sqrt{85}}{2*5}=\frac{5-\sqrt{85}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{85}}{2*5}=\frac{5+\sqrt{85}}{10}
$