(8x-9)(x+1)=-6

Solution for (8x-9)(x+1)=-6 equation:

(8x-9)(x+1)=-6

We move all terms to the left:

(8x-9)(x+1)-(-6)=0

We add all the numbers together, and all the variables

(8x-9)(x+1)+6=0

We multiply parentheses ..

(+8x^2+8x-9x-9)+6=0

We get rid of parentheses

8x^2+8x-9x-9+6=0

We add all the numbers together, and all the variables

8x^2-1x-3=0

a = 8; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·8·(-3)
Δ = 97
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{-(-1)-\sqrt{97}}{2*8}=\frac{1-\sqrt{97}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*8}=\frac{1+\sqrt{97}}{16}
$