10x^2-13-4=0

Solution for 10x^2-13-4=0 equation:

10x^2-13-4=0

We add all the numbers together, and all the variables

10x^2-17=0

a = 10; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·10·(-17)
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{170}}{2*10}=\frac{0-2\sqrt{170}}{20}
=-\frac{2\sqrt{170}}{20}
=-\frac{\sqrt{170}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{170}}{2*10}=\frac{0+2\sqrt{170}}{20}
=\frac{2\sqrt{170}}{20}
=\frac{\sqrt{170}}{10}
$