8x^2=-9x-1

Solution for 8x^2=-9x-1 equation:

8x^2=-9x-1

We move all terms to the left:

8x^2-(-9x-1)=0

We get rid of parentheses

8x^2+9x+1=0

a = 8; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·8·1
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*8}=\frac{-2}{16}
=-1/8
$