-4x^2+44x-114=0

Solution for -4x^2+44x-114=0 equation:

-4x^2+44x-114=0

a = -4; b = 44; c = -114;
Δ = b2-4ac
Δ = 442-4·(-4)·(-114)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{7}}{2*-4}=\frac{-44-4\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{7}}{2*-4}=\frac{-44+4\sqrt{7}}{-8}
$