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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(5(x+4)), so:

5(x+4)

We multiply parentheses

5x+20

Back to the equation:

-(5x+20)


We get rid of parentheses

-4x^2-20x-5x-20=0

We add all the numbers together, and all the variables

-4x^2-25x-20=0

a = -4; b = -25; c = -20;
Δ = b2-4ac
Δ = -252-4·(-4)·(-20)
Δ = 305
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{-(-25)-\sqrt{305}}{2*-4}=\frac{25-\sqrt{305}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{305}}{2*-4}=\frac{25+\sqrt{305}}{-8}
$