-4x^2-12x+42=0

Solution for -4x^2-12x+42=0 equation:

-4x^2-12x+42=0

a = -4; b = -12; c = +42;
Δ = b2-4ac
Δ = -122-4·(-4)·42
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{51}}{2*-4}=\frac{12-4\sqrt{51}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{51}}{2*-4}=\frac{12+4\sqrt{51}}{-8}
$