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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2-3x+2x-6)), so:

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

We get rid of parentheses

x^2-3x+2x-6

We add all the numbers together, and all the variables

x^2-1x-6

Back to the equation:

-(x^2-1x-6)


We add all the numbers together, and all the variables

5x^2+10x-(x^2-1x-6)=0

We get rid of parentheses

5x^2-x^2+10x+1x+6=0

We add all the numbers together, and all the variables

4x^2+11x+6=0

a = 4; b = 11; c = +6;
Δ = b2-4ac
Δ = 112-4·4·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*4}=\frac{-6}{8}
=-3/4
$