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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

3x(x+1)-9x

We add all the numbers together, and all the variables

-9x+3x(x+1)

We multiply parentheses

3x^2-9x+3x

We add all the numbers together, and all the variables

3x^2-6x

Back to the equation:

-(3x^2-6x)


We add all the numbers together, and all the variables

5x-(3x^2-6x)+7=0

We get rid of parentheses

-3x^2+5x+6x+7=0

We add all the numbers together, and all the variables

-3x^2+11x+7=0

a = -3; b = 11; c = +7;
Δ = b2-4ac
Δ = 112-4·(-3)·7
Δ = 205
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{-(11)-\sqrt{205}}{2*-3}=\frac{-11-\sqrt{205}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{205}}{2*-3}=\frac{-11+\sqrt{205}}{-6}
$