X(3x+2)=-2x(5+4x)

Solution for X(3x+2)=-2x(5+4x) equation:

X(3X+2)=-2X(5+4X)

We move all terms to the left:

X(3X+2)-(-2X(5+4X))=0

We add all the numbers together, and all the variables

X(3X+2)-(-2X(4X+5))=0

We multiply parentheses

3X^2+2X-(-2X(4X+5))=0


We calculate terms in parentheses: -(-2X(4X+5)), so:

-2X(4X+5)

We multiply parentheses

-8X^2-10X

Back to the equation:

-(-8X^2-10X)


We get rid of parentheses

3X^2+8X^2+10X+2X=0

We add all the numbers together, and all the variables

11X^2+12X=0

a = 11; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·11·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*11}=\frac{-24}{22}
=-1+1/11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*11}=\frac{0}{22}
=0
$