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}
$