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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(5x(x+3)), so:

5x(x+3)

We multiply parentheses

5x^2+15x

Back to the equation:

-(5x^2+15x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2-10x+15=0

a = -5; b = -10; c = +15;
Δ = b2-4ac
Δ = -102-4·(-5)·15
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*-5}=\frac{30}{-10}
=-3
$