3x^2-2x-5=9

Solution for 3x^2-2x-5=9 equation:

3x^2-2x-5=9

We move all terms to the left:

3x^2-2x-5-(9)=0

We add all the numbers together, and all the variables

3x^2-2x-14=0

a = 3; b = -2; c = -14;
Δ = b2-4ac
Δ = -22-4·3·(-14)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{43}}{2*3}=\frac{2-2\sqrt{43}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{43}}{2*3}=\frac{2+2\sqrt{43}}{6}
$