(x+2)(3x+5)=2x(x+9)

Solution for (x+2)(3x+5)=2x(x+9) equation:

(x+2)(3x+5)=2x(x+9)

We move all terms to the left:

(x+2)(3x+5)-(2x(x+9))=0

We multiply parentheses ..

(+3x^2+5x+6x+10)-(2x(x+9))=0


We calculate terms in parentheses: -(2x(x+9)), so:

2x(x+9)

We multiply parentheses

2x^2+18x

Back to the equation:

-(2x^2+18x)


We get rid of parentheses

3x^2-2x^2+5x+6x-18x+10=0

We add all the numbers together, and all the variables

x^2-7x+10=0

a = 1; b = -7; c = +10;
Δ = b2-4ac
Δ = -72-4·1·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*1}=\frac{10}{2}
=5
$