7x^2-14x-82=0

Solution for 7x^2-14x-82=0 equation:

7x^2-14x-82=0

a = 7; b = -14; c = -82;
Δ = b2-4ac
Δ = -142-4·7·(-82)
Δ = 2492
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:

$\sqrt{\Delta}=\sqrt{2492}=\sqrt{4*623}=\sqrt{4}*\sqrt{623}=2\sqrt{623}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{623}}{2*7}=\frac{14-2\sqrt{623}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{623}}{2*7}=\frac{14+2\sqrt{623}}{14}
$