4(2-x)(x+2)+20=36(x+1)-x(2x-17)

Solution for 4(2-x)(x+2)+20=36(x+1)-x(2x-17) equation:

4(2-x)(x+2)+20=36(x+1)-x(2x-17)

We move all terms to the left:

4(2-x)(x+2)+20-(36(x+1)-x(2x-17))=0

We add all the numbers together, and all the variables

4(-1x+2)(x+2)-(36(x+1)-x(2x-17))+20=0

We multiply parentheses ..

4(-1x^2-2x+2x+4)-(36(x+1)-x(2x-17))+20=0


We calculate terms in parentheses: -(36(x+1)-x(2x-17)), so:

36(x+1)-x(2x-17)

We multiply parentheses

-2x^2+36x+17x+36

We add all the numbers together, and all the variables

-2x^2+53x+36

Back to the equation:

-(-2x^2+53x+36)


We multiply parentheses

-4x^2-(-2x^2+53x+36)-8x+8x+16+20=0

We get rid of parentheses

-4x^2+2x^2-53x-8x+8x-36+16+20=0

We add all the numbers together, and all the variables

-2x^2-53x=0

a = -2; b = -53; c = 0;
Δ = b2-4ac
Δ = -532-4·(-2)·0
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-53}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+53}{2*-2}=\frac{106}{-4}
=-26+1/2
$