(9x-7)(4x+1)=0

Solution for (9x-7)(4x+1)=0 equation:

(9x-7)(4x+1)=0

We multiply parentheses ..

(+36x^2+9x-28x-7)=0

We get rid of parentheses

36x^2+9x-28x-7=0

We add all the numbers together, and all the variables

36x^2-19x-7=0

a = 36; b = -19; c = -7;
Δ = b2-4ac
Δ = -192-4·36·(-7)
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{-(-19)-37}{2*36}=\frac{-18}{72}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+37}{2*36}=\frac{56}{72}
=7/9
$