0=4x^2-4x-17

Solution for 0=4x^2-4x-17 equation:

0=4x^2-4x-17

We move all terms to the left:

0-(4x^2-4x-17)=0

We add all the numbers together, and all the variables

-(4x^2-4x-17)=0

We get rid of parentheses

-4x^2+4x+17=0

a = -4; b = 4; c = +17;
Δ = b2-4ac
Δ = 42-4·(-4)·17
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12\sqrt{2}}{2*-4}=\frac{-4-12\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12\sqrt{2}}{2*-4}=\frac{-4+12\sqrt{2}}{-8}
$