(6+2x-18)(2x-16)=(11-x)(x-3)

Solution for (6+2x-18)(2x-16)=(11-x)(x-3) equation:

(6+2x-18)(2x-16)=(11-x)(x-3)

We move all terms to the left:

(6+2x-18)(2x-16)-((11-x)(x-3))=0

We add all the numbers together, and all the variables

(2x-12)(2x-16)-((-1x+11)(x-3))=0

We multiply parentheses ..

(+4x^2-32x-24x+192)-((-1x+11)(x-3))=0


We calculate terms in parentheses: -((-1x+11)(x-3)), so:

(-1x+11)(x-3)

We multiply parentheses ..

(-1x^2+3x+11x-33)

We get rid of parentheses

-1x^2+3x+11x-33

We add all the numbers together, and all the variables

-1x^2+14x-33

Back to the equation:

-(-1x^2+14x-33)


We get rid of parentheses

4x^2+1x^2-32x-24x-14x+192+33=0

We add all the numbers together, and all the variables

5x^2-70x+225=0

a = 5; b = -70; c = +225;
Δ = b2-4ac
Δ = -702-4·5·225
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-20}{2*5}=\frac{50}{10}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+20}{2*5}=\frac{90}{10}
=9
$