7x^2-21x-56=0

Solution for 7x^2-21x-56=0 equation:

7x^2-21x-56=0

a = 7; b = -21; c = -56;
Δ = b2-4ac
Δ = -212-4·7·(-56)
Δ = 2009
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:

$\sqrt{\Delta}=\sqrt{2009}=\sqrt{49*41}=\sqrt{49}*\sqrt{41}=7\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-7\sqrt{41}}{2*7}=\frac{21-7\sqrt{41}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+7\sqrt{41}}{2*7}=\frac{21+7\sqrt{41}}{14}
$