5x(x+5)=9(4x+4)

Solution for 5x(x+5)=9(4x+4) equation:

5x(x+5)=9(4x+4)

We move all terms to the left:

5x(x+5)-(9(4x+4))=0

We multiply parentheses

5x^2+25x-(9(4x+4))=0


We calculate terms in parentheses: -(9(4x+4)), so:

9(4x+4)

We multiply parentheses

36x+36

Back to the equation:

-(36x+36)


We get rid of parentheses

5x^2+25x-36x-36=0

We add all the numbers together, and all the variables

5x^2-11x-36=0

a = 5; b = -11; c = -36;
Δ = b2-4ac
Δ = -112-4·5·(-36)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-29}{2*5}=\frac{-18}{10}
=-1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+29}{2*5}=\frac{40}{10}
=4
$