13b^2-8b-15=0

Solution for 13b^2-8b-15=0 equation:

13b^2-8b-15=0

a = 13; b = -8; c = -15;
Δ = b2-4ac
Δ = -82-4·13·(-15)
Δ = 844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{211}}{2*13}=\frac{8-2\sqrt{211}}{26}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{211}}{2*13}=\frac{8+2\sqrt{211}}{26}
$