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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(3x(x-2)-9), so:

3x(x-2)-9

We multiply parentheses

3x^2-6x-9

Back to the equation:

-(3x^2-6x-9)


We add all the numbers together, and all the variables

7x-(3x^2-6x-9)+2=0

We get rid of parentheses

-3x^2+7x+6x+9+2=0

We add all the numbers together, and all the variables

-3x^2+13x+11=0

a = -3; b = 13; c = +11;
Δ = b2-4ac
Δ = 132-4·(-3)·11
Δ = 301
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{301}}{2*-3}=\frac{-13-\sqrt{301}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{301}}{2*-3}=\frac{-13+\sqrt{301}}{-6}
$