(5x-1)(9+2x)=0

Solution for (5x-1)(9+2x)=0 equation:

(5x-1)(9+2x)=0

We add all the numbers together, and all the variables

(5x-1)(2x+9)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

10x^2+43x-9=0

a = 10; b = 43; c = -9;
Δ = b2-4ac
Δ = 432-4·10·(-9)
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*10}=\frac{-90}{20}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+47}{2*10}=\frac{4}{20}
=1/5
$