7*x^2-2*x-9=0

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

7*x^2-2x-9=0

We add all the numbers together, and all the variables

7x^2-2x-9=0

a = 7; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·7·(-9)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-16}{2*7}=\frac{-14}{14}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+16}{2*7}=\frac{18}{14}
=1+2/7
$