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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

x(2x+3)

We multiply parentheses

2x^2+3x

Back to the equation:

-(2x^2+3x)


We get rid of parentheses

-2x^2+2x-3x+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
$