x^2-4.5x+5.0625=2.0625

Solution for x^2-4.5x+5.0625=2.0625 equation:

x^2-4.5x+5.0625=2.0625

We move all terms to the left:

x^2-4.5x+5.0625-(2.0625)=0

We add all the numbers together, and all the variables

x^2-4.5x+3=0

a = 1; b = -4.5; c = +3;
Δ = b2-4ac
Δ = -4.52-4·1·3
Δ = 8.25
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{-(-4.5)-\sqrt{8.25}}{2*1}=\frac{4.5-\sqrt{8.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{8.25}}{2*1}=\frac{4.5+\sqrt{8.25}}{2}
$