x(x-2)=3x-5

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

x(x-2)=3x-5

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-5x+5=0

a = 1; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·1·5
Δ = 5
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{5}}{2*1}=\frac{5-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{5}}{2*1}=\frac{5+\sqrt{5}}{2}
$