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 = 5281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-\sqrt{5281}}{2*10}=\frac{59-\sqrt{5281}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{5281}}{2*10}=\frac{59+\sqrt{5281}}{20}
$