7x^2-2x-16=0

Solution for 7x^2-2x-16=0 equation:

7x^2-2x-16=0

a = 7; b = -2; c = -16;
Δ = b2-4ac
Δ = -22-4·7·(-16)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{113}}{2*7}=\frac{2-2\sqrt{113}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{113}}{2*7}=\frac{2+2\sqrt{113}}{14}
$