0=7x^2+9x-6x-54

Solution for 0=7x^2+9x-6x-54 equation:

0=7x^2+9x-6x-54

We move all terms to the left:

0-(7x^2+9x-6x-54)=0

We add all the numbers together, and all the variables

-(7x^2+9x-6x-54)=0

We get rid of parentheses

-7x^2-9x+6x+54=0

We add all the numbers together, and all the variables

-7x^2-3x+54=0

a = -7; b = -3; c = +54;
Δ = b2-4ac
Δ = -32-4·(-7)·54
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-39}{2*-7}=\frac{-36}{-14}
=2+4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+39}{2*-7}=\frac{42}{-14}
=-3
$