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

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

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

We move all terms to the left:

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

We multiply parentheses

5x-(2(x-3)(x+1))+15=0

We multiply parentheses ..

-(2(+x^2+x-3x-3))+5x+15=0


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

2(+x^2+x-3x-3)

We multiply parentheses

2x^2+2x-6x-6

We add all the numbers together, and all the variables

2x^2-4x-6

Back to the equation:

-(2x^2-4x-6)


We add all the numbers together, and all the variables

5x-(2x^2-4x-6)+15=0

We get rid of parentheses

-2x^2+5x+4x+6+15=0

We add all the numbers together, and all the variables

-2x^2+9x+21=0

a = -2; b = 9; c = +21;
Δ = b2-4ac
Δ = 92-4·(-2)·21
Δ = 249
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{-(9)-\sqrt{249}}{2*-2}=\frac{-9-\sqrt{249}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{249}}{2*-2}=\frac{-9+\sqrt{249}}{-4}
$