5x^2+2x-14=0

Solution for 5x^2+2x-14=0 equation:

5x^2+2x-14=0

a = 5; b = 2; c = -14;
Δ = b2-4ac
Δ = 22-4·5·(-14)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{71}}{2*5}=\frac{-2-2\sqrt{71}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{71}}{2*5}=\frac{-2+2\sqrt{71}}{10}
$