6(x^2-1)=x(7+8x)

Solution for 6(x^2-1)=x(7+8x) equation:

6(x^2-1)=x(7+8x)

We move all terms to the left:

6(x^2-1)-(x(7+8x))=0

We add all the numbers together, and all the variables

6(x^2-1)-(x(8x+7))=0

We multiply parentheses

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


We calculate terms in parentheses: -(x(8x+7)), so:

x(8x+7)

We multiply parentheses

8x^2+7x

Back to the equation:

-(8x^2+7x)


We get rid of parentheses

6x^2-8x^2-7x-6=0

We add all the numbers together, and all the variables

-2x^2-7x-6=0

a = -2; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·(-2)·(-6)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*-2}=\frac{6}{-4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*-2}=\frac{8}{-4}
=-2
$