13x^2+24x-1=14

Solution for 13x^2+24x-1=14 equation:

13x^2+24x-1=14

We move all terms to the left:

13x^2+24x-1-(14)=0

We add all the numbers together, and all the variables

13x^2+24x-15=0

a = 13; b = 24; c = -15;
Δ = b2-4ac
Δ = 242-4·13·(-15)
Δ = 1356
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:

$\sqrt{\Delta}=\sqrt{1356}=\sqrt{4*339}=\sqrt{4}*\sqrt{339}=2\sqrt{339}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{339}}{2*13}=\frac{-24-2\sqrt{339}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{339}}{2*13}=\frac{-24+2\sqrt{339}}{26}
$