4x(2x+1)=-5x(x-4)

Solution for 4x(2x+1)=-5x(x-4) equation:

4x(2x+1)=-5x(x-4)

We move all terms to the left:

4x(2x+1)-(-5x(x-4))=0

We multiply parentheses

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


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

-5x(x-4)

We multiply parentheses

-5x^2+20x

Back to the equation:

-(-5x^2+20x)


We get rid of parentheses

8x^2+5x^2-20x+4x=0

We add all the numbers together, and all the variables

13x^2-16x=0

a = 13; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·13·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*13}=\frac{0}{26}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*13}=\frac{32}{26}
=1+3/13
$