(3x^2)-2x-77=0

Solution for (3x^2)-2x-77=0 equation:

(3x^2)-2x-77=0

a = 3; b = -2; c = -77;
Δ = b2-4ac
Δ = -22-4·3·(-77)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{58}}{2*3}=\frac{2-4\sqrt{58}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{58}}{2*3}=\frac{2+4\sqrt{58}}{6}
$