(19-2x)(x+2)-(2x+9)(x+4)-4x(x+1)=0

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Solution for (19-2x)(x+2)-(2x+9)(x+4)-4x(x+1)=0 equation:



(19-2x)(x+2)-(2x+9)(x+4)-4x(x+1)=0
We add all the numbers together, and all the variables
(-2x+19)(x+2)-(2x+9)(x+4)-4x(x+1)=0
We multiply parentheses
-4x^2+(-2x+19)(x+2)-(2x+9)(x+4)-4x=0
We multiply parentheses ..
-4x^2+(-2x^2-4x+19x+38)-(2x+9)(x+4)-4x=0
We add all the numbers together, and all the variables
-4x^2+(-2x^2-4x+19x+38)-4x-(2x+9)(x+4)=0
We get rid of parentheses
-4x^2-2x^2-4x+19x-4x-(2x+9)(x+4)+38=0
We multiply parentheses ..
-4x^2-2x^2-(+2x^2+8x+9x+36)-4x+19x-4x+38=0
We add all the numbers together, and all the variables
-6x^2-(+2x^2+8x+9x+36)+11x+38=0
We get rid of parentheses
-6x^2-2x^2-8x-9x+11x-36+38=0
We add all the numbers together, and all the variables
-8x^2-6x+2=0
a = -8; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-8)·2
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*-8}=\frac{-4}{-16} =1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*-8}=\frac{16}{-16} =-1 $

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