0.4x+0.8(4)=0.5x(x+4)

Solution for 0.4x+0.8(4)=0.5x(x+4) equation:

0.4x+0.8(4)=0.5x(x+4)

We move all terms to the left:

0.4x+0.8(4)-(0.5x(x+4))=0


We calculate terms in parentheses: -(0.5x(x+4)), so:

0.5x(x+4)

We multiply parentheses

0x^2+0x

We add all the numbers together, and all the variables

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2+0.4x-x+0.84=0

We add all the numbers together, and all the variables

-1x^2-0.6x+0.84=0

a = -1; b = -0.6; c = +0.84;
Δ = b2-4ac
Δ = -0.62-4·(-1)·0.84
Δ = 3.72
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{-(-0.6)-\sqrt{3.72}}{2*-1}=\frac{0.6-\sqrt{3.72}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.6)+\sqrt{3.72}}{2*-1}=\frac{0.6+\sqrt{3.72}}{-2}
$