4w^2+6w-77=0

Solution for 4w^2+6w-77=0 equation:

4w^2+6w-77=0

a = 4; b = 6; c = -77;
Δ = b2-4ac
Δ = 62-4·4·(-77)
Δ = 1268
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1268}=\sqrt{4*317}=\sqrt{4}*\sqrt{317}=2\sqrt{317}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{317}}{2*4}=\frac{-6-2\sqrt{317}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{317}}{2*4}=\frac{-6+2\sqrt{317}}{8}
$