(((x^2)-(5*4)-7)/3)+6=9

Solution for (((x^2)-(5*4)-7)/3)+6=9 equation:

(((x^2)-(5*4)-7)/3)+6=9

We move all terms to the left:

(((x^2)-(5*4)-7)/3)+6-(9)=0

We add all the numbers together, and all the variables

((x^2-20-7)/3)+6-9=0

We add all the numbers together, and all the variables

((x^2-20-7)/3)-3=0

We multiply all the terms by the denominator


((x^2-20-7)-3*3)=0


We calculate terms in parentheses: +((x^2-20-7)-3*3), so:

(x^2-20-7)-3*3

We add all the numbers together, and all the variables

(x^2-20-7)-9

We get rid of parentheses

x^2-20-7-9

We add all the numbers together, and all the variables

x^2-36

Back to the equation:

+(x^2-36)


We get rid of parentheses

x^2-36=0

a = 1; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·1·(-36)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*1}=\frac{12}{2}
=6
$