7x^2-14x-17=0

Solution for 7x^2-14x-17=0 equation:

7x^2-14x-17=0

a = 7; b = -14; c = -17;
Δ = b2-4ac
Δ = -142-4·7·(-17)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{42}}{2*7}=\frac{14-4\sqrt{42}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{42}}{2*7}=\frac{14+4\sqrt{42}}{14}
$