4.0625=x^2-1.5x+0.5625

Solution for 4.0625=x^2-1.5x+0.5625 equation:

4.0625=x^2-1.5x+0.5625

We move all terms to the left:

4.0625-(x^2-1.5x+0.5625)=0

We get rid of parentheses

-x^2+1.5x-0.5625+4.0625=0

We add all the numbers together, and all the variables

-1x^2+1.5x+3.5=0

a = -1; b = 1.5; c = +3.5;
Δ = b2-4ac
Δ = 1.52-4·(-1)·3.5
Δ = 16.25
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{-(1.5)-\sqrt{16.25}}{2*-1}=\frac{-1.5-\sqrt{16.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{16.25}}{2*-1}=\frac{-1.5+\sqrt{16.25}}{-2}
$