17x^2-12x-3=6

Solution for 17x^2-12x-3=6 equation:

17x^2-12x-3=6

We move all terms to the left:

17x^2-12x-3-(6)=0

We add all the numbers together, and all the variables

17x^2-12x-9=0

a = 17; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·17·(-9)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{21}}{2*17}=\frac{12-6\sqrt{21}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{21}}{2*17}=\frac{12+6\sqrt{21}}{34}
$