4x^2-36x-77=0

Solution for 4x^2-36x-77=0 equation:

4x^2-36x-77=0

a = 4; b = -36; c = -77;
Δ = b2-4ac
Δ = -362-4·4·(-77)
Δ = 2528
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:

$\sqrt{\Delta}=\sqrt{2528}=\sqrt{16*158}=\sqrt{16}*\sqrt{158}=4\sqrt{158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{158}}{2*4}=\frac{36-4\sqrt{158}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{158}}{2*4}=\frac{36+4\sqrt{158}}{8}
$