13x^2-38-3=0

Solution for 13x^2-38-3=0 equation:

13x^2-38-3=0

We add all the numbers together, and all the variables

13x^2-41=0

a = 13; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·13·(-41)
Δ = 2132
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:

$\sqrt{\Delta}=\sqrt{2132}=\sqrt{4*533}=\sqrt{4}*\sqrt{533}=2\sqrt{533}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{533}}{2*13}=\frac{0-2\sqrt{533}}{26}
=-\frac{2\sqrt{533}}{26}
=-\frac{\sqrt{533}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{533}}{2*13}=\frac{0+2\sqrt{533}}{26}
=\frac{2\sqrt{533}}{26}
=\frac{\sqrt{533}}{13}
$