3x(x+9)=(x+8)(2x+5)

Solution for 3x(x+9)=(x+8)(2x+5) equation:

3x(x+9)=(x+8)(2x+5)

We move all terms to the left:

3x(x+9)-((x+8)(2x+5))=0

We multiply parentheses

3x^2+27x-((x+8)(2x+5))=0

We multiply parentheses ..

3x^2-((+2x^2+5x+16x+40))+27x=0


We calculate terms in parentheses: -((+2x^2+5x+16x+40)), so:

(+2x^2+5x+16x+40)

We get rid of parentheses

2x^2+5x+16x+40

We add all the numbers together, and all the variables

2x^2+21x+40

Back to the equation:

-(2x^2+21x+40)


We add all the numbers together, and all the variables

3x^2+27x-(2x^2+21x+40)=0

We get rid of parentheses

3x^2-2x^2+27x-21x-40=0

We add all the numbers together, and all the variables

x^2+6x-40=0

a = 1; b = 6; c = -40;
Δ = b2-4ac
Δ = 62-4·1·(-40)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*1}=\frac{8}{2}
=4
$