7x^2-21x-91=0

Solution for 7x^2-21x-91=0 equation:

7x^2-21x-91=0

a = 7; b = -21; c = -91;
Δ = b2-4ac
Δ = -212-4·7·(-91)
Δ = 2989
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:

$\sqrt{\Delta}=\sqrt{2989}=\sqrt{49*61}=\sqrt{49}*\sqrt{61}=7\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-7\sqrt{61}}{2*7}=\frac{21-7\sqrt{61}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+7\sqrt{61}}{2*7}=\frac{21+7\sqrt{61}}{14}
$