(4x+5)(-x+4)-(4x+8)(4x+5)=0

Solution for (4x+5)(-x+4)-(4x+8)(4x+5)=0 equation:

(4x+5)(-x+4)-(4x+8)(4x+5)=0

We add all the numbers together, and all the variables

(4x+5)(-1x+4)-(4x+8)(4x+5)=0

We multiply parentheses ..

(-4x^2+16x-5x+20)-(4x+8)(4x+5)=0

We get rid of parentheses

-4x^2+16x-5x-(4x+8)(4x+5)+20=0

We multiply parentheses ..

-4x^2-(+16x^2+20x+32x+40)+16x-5x+20=0

We add all the numbers together, and all the variables

-4x^2-(+16x^2+20x+32x+40)+11x+20=0

We get rid of parentheses

-4x^2-16x^2-20x-32x+11x-40+20=0

We add all the numbers together, and all the variables

-20x^2-41x-20=0

a = -20; b = -41; c = -20;
Δ = b2-4ac
Δ = -412-4·(-20)·(-20)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-9}{2*-20}=\frac{32}{-40}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+9}{2*-20}=\frac{50}{-40}
=-1+1/4
$