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

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

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

We move all terms to the left:

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

We multiply parentheses

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

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

We add all the numbers together, and all the variables

5x^2-12x+4=0

a = 5; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·5·4
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8}{2*5}=\frac{4}{10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8}{2*5}=\frac{20}{10}
=2
$