10x^2-19=-5

Solution for 10x^2-19=-5 equation:

10x^2-19=-5

We move all terms to the left:

10x^2-19-(-5)=0

We add all the numbers together, and all the variables

10x^2-14=0

a = 10; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·10·(-14)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{35}}{2*10}=\frac{0-4\sqrt{35}}{20}
=-\frac{4\sqrt{35}}{20}
=-\frac{\sqrt{35}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{35}}{2*10}=\frac{0+4\sqrt{35}}{20}
=\frac{4\sqrt{35}}{20}
=\frac{\sqrt{35}}{5}
$