(4x-5)(x+8)/(x-9)=0

Solution for (4x-5)(x+8)/(x-9)=0 equation:

(4x-5)(x+8)/(x-9)=0


Domain of the equation: (x-9)!=0

We move all terms containing x to the left, all other terms to the right

x!=9

x∈R


We multiply parentheses ..

(+4x^2+32x-5x-40)/(x-9)=0

We multiply all the terms by the denominator


(+4x^2+32x-5x-40)=0

We get rid of parentheses

4x^2+32x-5x-40=0

We add all the numbers together, and all the variables

4x^2+27x-40=0

a = 4; b = 27; c = -40;
Δ = b2-4ac
Δ = 272-4·4·(-40)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-37}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+37}{2*4}=\frac{10}{8}
=1+1/4
$