0=9x^2-7x-1

Solution for 0=9x^2-7x-1 equation:

0=9x^2-7x-1

We move all terms to the left:

0-(9x^2-7x-1)=0

We add all the numbers together, and all the variables

-(9x^2-7x-1)=0

We get rid of parentheses

-9x^2+7x+1=0

a = -9; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-9)·1
Δ = 85
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{-(7)-\sqrt{85}}{2*-9}=\frac{-7-\sqrt{85}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{85}}{2*-9}=\frac{-7+\sqrt{85}}{-18}
$