8x=-5x(3+x)

Solution for 8x=-5x(3+x) equation:

8x=-5x(3+x)

We move all terms to the left:

8x-(-5x(3+x))=0

We add all the numbers together, and all the variables

8x-(-5x(x+3))=0


We calculate terms in parentheses: -(-5x(x+3)), so:

-5x(x+3)

We multiply parentheses

-5x^2-15x

Back to the equation:

-(-5x^2-15x)


We get rid of parentheses

5x^2+15x+8x=0

We add all the numbers together, and all the variables

5x^2+23x=0

a = 5; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·5·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*5}=\frac{-46}{10}
=-4+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*5}=\frac{0}{10}
=0
$