0=4x^2+9x-1

Solution for 0=4x^2+9x-1 equation:

0=4x^2+9x-1

We move all terms to the left:

0-(4x^2+9x-1)=0

We add all the numbers together, and all the variables

-(4x^2+9x-1)=0

We get rid of parentheses

-4x^2-9x+1=0

a = -4; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-4)·1
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{-(-9)-\sqrt{97}}{2*-4}=\frac{9-\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{97}}{2*-4}=\frac{9+\sqrt{97}}{-8}
$