x*(5-x)=2.25

Solution for x*(5-x)=2.25 equation:

x(5-x)=2.25

We move all terms to the left:

x(5-x)-(2.25)=0

We add all the numbers together, and all the variables

x(-1x+5)-(2.25)=0

We add all the numbers together, and all the variables

x(-1x+5)-2.25=0

We multiply parentheses

-1x^2+5x-2.25=0

a = -1; b = 5; c = -2.25;
Δ = b2-4ac
Δ = 52-4·(-1)·(-2.25)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-4}{2*-1}=\frac{-9}{-2}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+4}{2*-1}=\frac{-1}{-2}
=1/2
$