-(9x+14)(x-6)=0

Solution for -(9x+14)(x-6)=0 equation:

-(9x+14)(x-6)=0

We multiply parentheses ..

-(+9x^2-54x+14x-84)=0

We get rid of parentheses

-9x^2+54x-14x+84=0

We add all the numbers together, and all the variables

-9x^2+40x+84=0

a = -9; b = 40; c = +84;
Δ = b2-4ac
Δ = 402-4·(-9)·84
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-68}{2*-9}=\frac{-108}{-18}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+68}{2*-9}=\frac{28}{-18}
=-1+5/9
$