2x(x+9)=(1x-5)(x+9)

Solution for 2x(x+9)=(1x-5)(x+9) equation:

2x(x+9)=(1x-5)(x+9)

We move all terms to the left:

2x(x+9)-((1x-5)(x+9))=0

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2+18x-((x-5)(x+9))=0

We multiply parentheses ..

2x^2-((+x^2+9x-5x-45))+18x=0


We calculate terms in parentheses: -((+x^2+9x-5x-45)), so:

(+x^2+9x-5x-45)

We get rid of parentheses

x^2+9x-5x-45

We add all the numbers together, and all the variables

x^2+4x-45

Back to the equation:

-(x^2+4x-45)


We add all the numbers together, and all the variables

2x^2+18x-(x^2+4x-45)=0

We get rid of parentheses

2x^2-x^2+18x-4x+45=0

We add all the numbers together, and all the variables

x^2+14x+45=0

a = 1; b = 14; c = +45;
Δ = b2-4ac
Δ = 142-4·1·45
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4}{2*1}=\frac{-10}{2}
=-5
$