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

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

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

We move all terms to the left:

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

We multiply parentheses

2x-((x+2)(x+3))+10=0

We multiply parentheses ..

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

Back to the equation:

-(x^2+5x+6)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-3x+4=0

a = -1; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-1)·4
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{-(-3)-5}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*-1}=\frac{8}{-2}
=-4
$