0=4x^2-9x-5

Solution for 0=4x^2-9x-5 equation:

0=4x^2-9x-5

We move all terms to the left:

0-(4x^2-9x-5)=0

We add all the numbers together, and all the variables

-(4x^2-9x-5)=0

We get rid of parentheses

-4x^2+9x+5=0

a = -4; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·(-4)·5
Δ = 161
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{161}}{2*-4}=\frac{-9-\sqrt{161}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{161}}{2*-4}=\frac{-9+\sqrt{161}}{-8}
$