-10x^2+19=0

Solution for -10x^2+19=0 equation:

-10x^2+19=0

a = -10; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-10)·19
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{190}}{2*-10}=\frac{0-2\sqrt{190}}{-20}
=-\frac{2\sqrt{190}}{-20}
=-\frac{\sqrt{190}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{190}}{2*-10}=\frac{0+2\sqrt{190}}{-20}
=\frac{2\sqrt{190}}{-20}
=\frac{\sqrt{190}}{-10}
$