9x(x-5)=8(x+5)

Solution for 9x(x-5)=8(x+5) equation:

9x(x-5)=8(x+5)

We move all terms to the left:

9x(x-5)-(8(x+5))=0

We multiply parentheses

9x^2-45x-(8(x+5))=0


We calculate terms in parentheses: -(8(x+5)), so:

8(x+5)

We multiply parentheses

8x+40

Back to the equation:

-(8x+40)


We get rid of parentheses

9x^2-45x-8x-40=0

We add all the numbers together, and all the variables

9x^2-53x-40=0

a = 9; b = -53; c = -40;
Δ = b2-4ac
Δ = -532-4·9·(-40)
Δ = 4249
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{-(-53)-\sqrt{4249}}{2*9}=\frac{53-\sqrt{4249}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{4249}}{2*9}=\frac{53+\sqrt{4249}}{18}
$