8x^2+14x-2=0

Solution for 8x^2+14x-2=0 equation:

8x^2+14x-2=0

a = 8; b = 14; c = -2;
Δ = b2-4ac
Δ = 142-4·8·(-2)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{65}}{2*8}=\frac{-14-2\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{65}}{2*8}=\frac{-14+2\sqrt{65}}{16}
$