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

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

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

We move all terms to the left:

3x(x+2)-(-2(-x-5))=0

We add all the numbers together, and all the variables

3x(x+2)-(-2(-1x-5))=0

We multiply parentheses

3x^2+6x-(-2(-1x-5))=0


We calculate terms in parentheses: -(-2(-1x-5)), so:

-2(-1x-5)

We multiply parentheses

2x+10

Back to the equation:

-(2x+10)


We get rid of parentheses

3x^2+6x-2x-10=0

We add all the numbers together, and all the variables

3x^2+4x-10=0

a = 3; b = 4; c = -10;
Δ = b2-4ac
Δ = 42-4·3·(-10)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{34}}{2*3}=\frac{-4-2\sqrt{34}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{34}}{2*3}=\frac{-4+2\sqrt{34}}{6}
$