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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2-20x-(9(x-5))=0


We calculate terms in parentheses: -(9(x-5)), so:

9(x-5)

We multiply parentheses

9x-45

Back to the equation:

-(9x-45)


We get rid of parentheses

4x^2-20x-9x+45=0

We add all the numbers together, and all the variables

4x^2-29x+45=0

a = 4; b = -29; c = +45;
Δ = b2-4ac
Δ = -292-4·4·45
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-11}{2*4}=\frac{18}{8}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+11}{2*4}=\frac{40}{8}
=5
$