2x(x+2)=5(x+2)

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

2x(x+2)=5(x+2)

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(5(x+2)), so:

5(x+2)

We multiply parentheses

5x+10

Back to the equation:

-(5x+10)


We get rid of parentheses

2x^2+4x-5x-10=0

We add all the numbers together, and all the variables

2x^2-1x-10=0

a = 2; b = -1; c = -10;
Δ = b2-4ac
Δ = -12-4·2·(-10)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*2}=\frac{10}{4}
=2+1/2
$