7(x-8)-8x(x+7)=x+7-(x-6)

Solution for 7(x-8)-8x(x+7)=x+7-(x-6) equation:

7(x-8)-8x(x+7)=x+7-(x-6)

We move all terms to the left:

7(x-8)-8x(x+7)-(x+7-(x-6))=0

We multiply parentheses

-8x^2+7x-56x-(x+7-(x-6))-56=0


We calculate terms in parentheses: -(x+7-(x-6)), so:

x+7-(x-6)

determiningTheFunctionDomain
x-(x-6)+7

We get rid of parentheses

x-x+6+7

We add all the numbers together, and all the variables

13

Back to the equation:

-(13)


We add all the numbers together, and all the variables

-8x^2-49x-69=0

a = -8; b = -49; c = -69;
Δ = b2-4ac
Δ = -492-4·(-8)·(-69)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-\sqrt{193}}{2*-8}=\frac{49-\sqrt{193}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{193}}{2*-8}=\frac{49+\sqrt{193}}{-16}
$