(X-2)(4x+5)-2x(x-4)=-5

Solution for (X-2)(4x+5)-2x(x-4)=-5 equation:

(X-2)(4X+5)-2X(X-4)=-5

We move all terms to the left:

(X-2)(4X+5)-2X(X-4)-(-5)=0

We add all the numbers together, and all the variables

(X-2)(4X+5)-2X(X-4)+5=0

We multiply parentheses

-2X^2+(X-2)(4X+5)+8X+5=0

We multiply parentheses ..

-2X^2+(+4X^2+5X-8X-10)+8X+5=0

We get rid of parentheses

-2X^2+4X^2+5X-8X+8X-10+5=0

We add all the numbers together, and all the variables

2X^2+5X-5=0

a = 2; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·2·(-5)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{65}}{2*2}=\frac{-5-\sqrt{65}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*2}=\frac{-5+\sqrt{65}}{4}
$