4x^2-144x+14=0

Solution for 4x^2-144x+14=0 equation:

4x^2-144x+14=0

a = 4; b = -144; c = +14;
Δ = b2-4ac
Δ = -1442-4·4·14
Δ = 20512
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:

$\sqrt{\Delta}=\sqrt{20512}=\sqrt{16*1282}=\sqrt{16}*\sqrt{1282}=4\sqrt{1282}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1282}}{2*4}=\frac{144-4\sqrt{1282}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1282}}{2*4}=\frac{144+4\sqrt{1282}}{8}
$