(7x-9)(13+4x)=0

Solution for (7x-9)(13+4x)=0 equation:

(7x-9)(13+4x)=0

We add all the numbers together, and all the variables

(7x-9)(4x+13)=0

We multiply parentheses ..

(+28x^2+91x-36x-117)=0

We get rid of parentheses

28x^2+91x-36x-117=0

We add all the numbers together, and all the variables

28x^2+55x-117=0

a = 28; b = 55; c = -117;
Δ = b2-4ac
Δ = 552-4·28·(-117)
Δ = 16129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16129}=127$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-127}{2*28}=\frac{-182}{56}
=-3+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+127}{2*28}=\frac{72}{56}
=1+2/7
$