13x2-10x-12=0

Solution for 13x2-10x-12=0 equation:

13x^2-10x-12=0

a = 13; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·13·(-12)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{181}}{2*13}=\frac{10-2\sqrt{181}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{181}}{2*13}=\frac{10+2\sqrt{181}}{26}
$