9x-(3+2)=2x(2x-2)+4

Solution for 9x-(3+2)=2x(2x-2)+4 equation:

9x-(3+2)=2x(2x-2)+4

We move all terms to the left:

9x-(3+2)-(2x(2x-2)+4)=0

We add all the numbers together, and all the variables

9x-(2x(2x-2)+4)-5=0


We calculate terms in parentheses: -(2x(2x-2)+4), so:

2x(2x-2)+4

We multiply parentheses

4x^2-4x+4

Back to the equation:

-(4x^2-4x+4)


We get rid of parentheses

-4x^2+9x+4x-4-5=0

We add all the numbers together, and all the variables

-4x^2+13x-9=0

a = -4; b = 13; c = -9;
Δ = b2-4ac
Δ = 132-4·(-4)·(-9)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5}{2*-4}=\frac{-18}{-8}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*-4}=\frac{-8}{-8}
=1
$