-5x(x+2)=3(x+1)-9

Solution for -5x(x+2)=3(x+1)-9 equation:

-5x(x+2)=3(x+1)-9

We move all terms to the left:

-5x(x+2)-(3(x+1)-9)=0

We multiply parentheses

-5x^2-10x-(3(x+1)-9)=0


We calculate terms in parentheses: -(3(x+1)-9), so:

3(x+1)-9

We multiply parentheses

3x+3-9

We add all the numbers together, and all the variables

3x-6

Back to the equation:

-(3x-6)


We get rid of parentheses

-5x^2-10x-3x+6=0

We add all the numbers together, and all the variables

-5x^2-13x+6=0

a = -5; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·(-5)·6
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*-5}=\frac{-4}{-10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*-5}=\frac{30}{-10}
=-3
$