0.2x(x+1)+0.5x=-0.3x(x-4)

Solution for 0.2x(x+1)+0.5x=-0.3x(x-4) equation:

0.2x(x+1)+0.5x=-0.3x(x-4)

We move all terms to the left:

0.2x(x+1)+0.5x-(-0.3x(x-4))=0

We add all the numbers together, and all the variables

0.5x+0.2x(x+1)-(-0.3x(x-4))=0

We multiply parentheses

0x^2+0.5x+0x-(-0.3x(x-4))=0


We calculate terms in parentheses: -(-0.3x(x-4)), so:

-0.3x(x-4)

We multiply parentheses

-0x^2-0x

We add all the numbers together, and all the variables

-1x^2-1x

Back to the equation:

-(-1x^2-1x)


We add all the numbers together, and all the variables

x^2-(-1x^2-1x)+1.5x=0

We get rid of parentheses

x^2+1x^2+1x+1.5x=0

We add all the numbers together, and all the variables

2x^2+2.5x=0

a = 2; b = 2.5; c = 0;
Δ = b2-4ac
Δ = 2.52-4·2·0
Δ = 6.25
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{-(2.5)-\sqrt{6.25}}{2*2}=\frac{-2.5-\sqrt{6.25}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{6.25}}{2*2}=\frac{-2.5+\sqrt{6.25}}{4}
$