3x2-x-127=0

Solution for 3x2-x-127=0 equation:

3x^2-x-127=0

We add all the numbers together, and all the variables

3x^2-1x-127=0

a = 3; b = -1; c = -127;
Δ = b2-4ac
Δ = -12-4·3·(-127)
Δ = 1525
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:

$\sqrt{\Delta}=\sqrt{1525}=\sqrt{25*61}=\sqrt{25}*\sqrt{61}=5\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{61}}{2*3}=\frac{1-5\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{61}}{2*3}=\frac{1+5\sqrt{61}}{6}
$