3x^2-16x-77=0

Solution for 3x^2-16x-77=0 equation:

3x^2-16x-77=0

a = 3; b = -16; c = -77;
Δ = b2-4ac
Δ = -162-4·3·(-77)
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{295}}{2*3}=\frac{16-2\sqrt{295}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{295}}{2*3}=\frac{16+2\sqrt{295}}{6}
$