(X-5)(9x+2)=0

Solution for (X-5)(9x+2)=0 equation:

(X-5)(9X+2)=0

We multiply parentheses ..

(+9X^2+2X-45X-10)=0

We get rid of parentheses

9X^2+2X-45X-10=0

We add all the numbers together, and all the variables

9X^2-43X-10=0

a = 9; b = -43; c = -10;
Δ = b2-4ac
Δ = -432-4·9·(-10)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-47}{2*9}=\frac{-4}{18}
=-2/9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+47}{2*9}=\frac{90}{18}
=5
$