0=-4x^2-9x+34

Solution for 0=-4x^2-9x+34 equation:

0=-4x^2-9x+34

We move all terms to the left:

0-(-4x^2-9x+34)=0

We add all the numbers together, and all the variables

-(-4x^2-9x+34)=0

We get rid of parentheses

4x^2+9x-34=0

a = 4; b = 9; c = -34;
Δ = b2-4ac
Δ = 92-4·4·(-34)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-25}{2*4}=\frac{-34}{8}
=-4+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+25}{2*4}=\frac{16}{8}
=2
$