13x+17x^2-13=0

Solution for 13x+17x^2-13=0 equation:

13x+17x^2-13=0

a = 17; b = 13; c = -13;
Δ = b2-4ac
Δ = 132-4·17·(-13)
Δ = 1053
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:

$\sqrt{\Delta}=\sqrt{1053}=\sqrt{81*13}=\sqrt{81}*\sqrt{13}=9\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-9\sqrt{13}}{2*17}=\frac{-13-9\sqrt{13}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+9\sqrt{13}}{2*17}=\frac{-13+9\sqrt{13}}{34}
$