4x(x+9)=(3x+4)(x+9)

Solution for 4x(x+9)=(3x+4)(x+9) equation:

4x(x+9)=(3x+4)(x+9)

We move all terms to the left:

4x(x+9)-((3x+4)(x+9))=0

We multiply parentheses

4x^2+36x-((3x+4)(x+9))=0

We multiply parentheses ..

4x^2-((+3x^2+27x+4x+36))+36x=0


We calculate terms in parentheses: -((+3x^2+27x+4x+36)), so:

(+3x^2+27x+4x+36)

We get rid of parentheses

3x^2+27x+4x+36

We add all the numbers together, and all the variables

3x^2+31x+36

Back to the equation:

-(3x^2+31x+36)


We add all the numbers together, and all the variables

4x^2+36x-(3x^2+31x+36)=0

We get rid of parentheses

4x^2-3x^2+36x-31x-36=0

We add all the numbers together, and all the variables

x^2+5x-36=0

a = 1; b = 5; c = -36;
Δ = b2-4ac
Δ = 52-4·1·(-36)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*1}=\frac{8}{2}
=4
$