13x^2+3x-8=0

Solution for 13x^2+3x-8=0 equation:

13x^2+3x-8=0

a = 13; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·13·(-8)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5\sqrt{17}}{2*13}=\frac{-3-5\sqrt{17}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5\sqrt{17}}{2*13}=\frac{-3+5\sqrt{17}}{26}
$