4-2(2.5x-8.5)=(x-3)(x-3)

Solution for 4-2(2.5x-8.5)=(x-3)(x-3) equation:

4-2(2.5x-8.5)=(x-3)(x-3)

We move all terms to the left:

4-2(2.5x-8.5)-((x-3)(x-3))=0

We multiply parentheses

-4x-((x-3)(x-3))+17+4=0

We multiply parentheses ..

-((+x^2-3x-3x+9))-4x+17+4=0


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

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

We get rid of parentheses

x^2-3x-3x+9

We add all the numbers together, and all the variables

x^2-6x+9

Back to the equation:

-(x^2-6x+9)


We add all the numbers together, and all the variables

-4x-(x^2-6x+9)+21=0

We get rid of parentheses

-x^2-4x+6x-9+21=0

We add all the numbers together, and all the variables

-1x^2+2x+12=0

a = -1; b = 2; c = +12;
Δ = b2-4ac
Δ = 22-4·(-1)·12
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*-1}=\frac{-2-2\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*-1}=\frac{-2+2\sqrt{13}}{-2}
$