X+13x2=5

Solution for X+13x2=5 equation:

X+13X^2=5

We move all terms to the left:

X+13X^2-(5)=0

a = 13; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·13·(-5)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{29}}{2*13}=\frac{-1-3\sqrt{29}}{26}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{29}}{2*13}=\frac{-1+3\sqrt{29}}{26}
$