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

Solution for x(2-x)+3x-5=0 equation:

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

We add all the numbers together, and all the variables

x(-1x+2)+3x-5=0

We add all the numbers together, and all the variables

3x+x(-1x+2)-5=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-1x^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}
$