7x^2-16x-108=0

Solution for 7x^2-16x-108=0 equation:

7x^2-16x-108=0

a = 7; b = -16; c = -108;
Δ = b2-4ac
Δ = -162-4·7·(-108)
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{205}}{2*7}=\frac{16-4\sqrt{205}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{205}}{2*7}=\frac{16+4\sqrt{205}}{14}
$