(x+9)(4x+-1)=0

Solution for (x+9)(4x+-1)=0 equation:

(x+9)(4x+-1)=0

We add all the numbers together, and all the variables

(x+9)(4x-1)=0

We multiply parentheses ..

(+4x^2-1x+36x-9)=0

We get rid of parentheses

4x^2-1x+36x-9=0

We add all the numbers together, and all the variables

4x^2+35x-9=0

a = 4; b = 35; c = -9;
Δ = b2-4ac
Δ = 352-4·4·(-9)
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{-(35)-37}{2*4}=\frac{-72}{8}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+37}{2*4}=\frac{2}{8}
=1/4
$