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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: +((x^2-(+5*4x)-7)-3*3), so:

(x^2-(+5*4x)-7)-3*3

We add all the numbers together, and all the variables

(x^2-(+5*4x)-7)-9


We calculate terms in parentheses: +(x^2-(+5*4x)-7), so:

x^2-(+5*4x)-7

We get rid of parentheses

x^2-5*4x-7

Wy multiply elements

x^2-20x-7

Back to the equation:

+(x^2-20x-7)


We get rid of parentheses

x^2-20x-7-9

We add all the numbers together, and all the variables

x^2-20x-16

Back to the equation:

+(x^2-20x-16)


We get rid of parentheses

x^2-20x-16=0

a = 1; b = -20; c = -16;
Δ = b2-4ac
Δ = -202-4·1·(-16)
Δ = 464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{29}}{2*1}=\frac{20-4\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{29}}{2*1}=\frac{20+4\sqrt{29}}{2}
$