-2x^2+71=0

Solution for -2x^2+71=0 equation:

-2x^2+71=0

a = -2; b = 0; c = +71;
Δ = b2-4ac
Δ = 02-4·(-2)·71
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{142}}{2*-2}=\frac{0-2\sqrt{142}}{-4}
=-\frac{2\sqrt{142}}{-4}
=-\frac{\sqrt{142}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{142}}{2*-2}=\frac{0+2\sqrt{142}}{-4}
=\frac{2\sqrt{142}}{-4}
=\frac{\sqrt{142}}{-2}
$