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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

x-((-2x+3)(-1x+3))=0

We multiply parentheses ..

-((+2x^2-6x-3x+9))+x=0


We calculate terms in parentheses: -((+2x^2-6x-3x+9)), so:

(+2x^2-6x-3x+9)

We get rid of parentheses

2x^2-6x-3x+9

We add all the numbers together, and all the variables

2x^2-9x+9

Back to the equation:

-(2x^2-9x+9)


We add all the numbers together, and all the variables

x-(2x^2-9x+9)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+10x-9=0

a = -2; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·(-2)·(-9)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{7}}{2*-2}=\frac{-10-2\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{7}}{2*-2}=\frac{-10+2\sqrt{7}}{-4}
$