(9x-7)(x+6)=0

Solution for (9x-7)(x+6)=0 equation:

(9x-7)(x+6)=0

We multiply parentheses ..

(+9x^2+54x-7x-42)=0

We get rid of parentheses

9x^2+54x-7x-42=0

We add all the numbers together, and all the variables

9x^2+47x-42=0

a = 9; b = 47; c = -42;
Δ = b2-4ac
Δ = 472-4·9·(-42)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-61}{2*9}=\frac{-108}{18}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+61}{2*9}=\frac{14}{18}
=7/9
$