13x^2-12x-3=6

Solution for 13x^2-12x-3=6 equation:

13x^2-12x-3=6

We move all terms to the left:

13x^2-12x-3-(6)=0

We add all the numbers together, and all the variables

13x^2-12x-9=0

a = 13; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·13·(-9)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{17}}{2*13}=\frac{12-6\sqrt{17}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{17}}{2*13}=\frac{12+6\sqrt{17}}{26}
$