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

Solution for (2x-9)(4x+1)=0 equation:

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

We multiply parentheses ..

(+8x^2+2x-36x-9)=0

We get rid of parentheses

8x^2+2x-36x-9=0

We add all the numbers together, and all the variables

8x^2-34x-9=0

a = 8; b = -34; c = -9;
Δ = b2-4ac
Δ = -342-4·8·(-9)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-38}{2*8}=\frac{-4}{16}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+38}{2*8}=\frac{72}{16}
=4+1/2
$