x-(2-0.2)^2=5.8-(2x+0.1)(2x-0.1)

Solution for x-(2-0.2)^2=5.8-(2x+0.1)(2x-0.1) equation:

x-(2-0.2)^2=5.8-(2x+0.1)(2x-0.1)

We move all terms to the left:

x-(2-0.2)^2-(5.8-(2x+0.1)(2x-0.1))=0

We add all the numbers together, and all the variables

x-(5.8-(2x+0.1)(2x-0.1))-(1.8)^2=0

We add all the numbers together, and all the variables

x-(5.8-(2x+0.1)(2x-0.1))-3.24=0

We use the square of the difference formula

4x^2+x+0.01-3.24=0

We add all the numbers together, and all the variables

4x^2+x-3.23=0

a = 4; b = 1; c = -3.23;
Δ = b2-4ac
Δ = 12-4·4·(-3.23)
Δ = 52.68
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)-\sqrt{52.68}}{2*4}=\frac{-1-\sqrt{52.68}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{52.68}}{2*4}=\frac{-1+\sqrt{52.68}}{8}
$