X(x-1)=5x-3

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

X(X-1)=5X-3

We move all terms to the left:

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

We multiply parentheses

X^2-1X-(5X-3)=0

We get rid of parentheses

X^2-1X-5X+3=0

We add all the numbers together, and all the variables

X^2-6X+3=0

a = 1; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·1·3
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{6}}{2*1}=\frac{6-2\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{6}}{2*1}=\frac{6+2\sqrt{6}}{2}
$