3x^2+8x-77=0

Solution for 3x^2+8x-77=0 equation:

3x^2+8x-77=0

a = 3; b = 8; c = -77;
Δ = b2-4ac
Δ = 82-4·3·(-77)
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{247}}{2*3}=\frac{-8-2\sqrt{247}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{247}}{2*3}=\frac{-8+2\sqrt{247}}{6}
$