-4x^2-12x+112=0

Solution for -4x^2-12x+112=0 equation:

-4x^2-12x+112=0

a = -4; b = -12; c = +112;
Δ = b2-4ac
Δ = -122-4·(-4)·112
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-44}{2*-4}=\frac{-32}{-8}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+44}{2*-4}=\frac{56}{-8}
=-7
$