5x-x*x=5,25

Solution for 5x-x*x=5,25 equation:

5x-x*x=5.25

We move all terms to the left:

5x-x*x-(5.25)=0

We add all the numbers together, and all the variables

5x-x*x-5.25=0

Wy multiply elements

-1x^2+5x-5.25=0

a = -1; b = 5; c = -5.25;
Δ = b2-4ac
Δ = 52-4·(-1)·(-5.25)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-2}{2*-1}=\frac{-7}{-2}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+2}{2*-1}=\frac{-3}{-2}
=1+1/2
$