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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

2(x+5)

We multiply parentheses

2x+10

Back to the equation:

-(2x+10)


We add all the numbers together, and all the variables

-2x^2-7x-(2x+10)=0

We get rid of parentheses

-2x^2-7x-2x-10=0

We add all the numbers together, and all the variables

-2x^2-9x-10=0

a = -2; b = -9; c = -10;
Δ = b2-4ac
Δ = -92-4·(-2)·(-10)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*-2}=\frac{8}{-4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*-2}=\frac{10}{-4}
=-2+1/2
$