10x(x-5)=9(x-5)

Solution for 10x(x-5)=9(x-5) equation:

10x(x-5)=9(x-5)

We move all terms to the left:

10x(x-5)-(9(x-5))=0

We multiply parentheses

10x^2-50x-(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

10x^2-50x-9x+45=0

We add all the numbers together, and all the variables

10x^2-59x+45=0

a = 10; b = -59; c = +45;
Δ = b2-4ac
Δ = -592-4·10·45
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-41}{2*10}=\frac{18}{20}
=9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+41}{2*10}=\frac{100}{20}
=5
$