-5x^2-2=14x

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

-5x^2-2=14x

We move all terms to the left:

-5x^2-2-(14x)=0

a = -5; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·(-5)·(-2)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{39}}{2*-5}=\frac{14-2\sqrt{39}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*-5}=\frac{14+2\sqrt{39}}{-10}
$