-4x^2-32x+67=0

Solution for -4x^2-32x+67=0 equation:

-4x^2-32x+67=0

a = -4; b = -32; c = +67;
Δ = b2-4ac
Δ = -322-4·(-4)·67
Δ = 2096
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:

$\sqrt{\Delta}=\sqrt{2096}=\sqrt{16*131}=\sqrt{16}*\sqrt{131}=4\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{131}}{2*-4}=\frac{32-4\sqrt{131}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{131}}{2*-4}=\frac{32+4\sqrt{131}}{-8}
$