7x^2-28x-6=0

Solution for 7x^2-28x-6=0 equation:

7x^2-28x-6=0

a = 7; b = -28; c = -6;
Δ = b2-4ac
Δ = -282-4·7·(-6)
Δ = 952
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:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{238}}{2*7}=\frac{28-2\sqrt{238}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{238}}{2*7}=\frac{28+2\sqrt{238}}{14}
$