4X^2-66x+122=0

Solution for 4X^2-66x+122=0 equation:

4X^2-66X+122=0

a = 4; b = -66; c = +122;
Δ = b2-4ac
Δ = -662-4·4·122
Δ = 2404
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:

$\sqrt{\Delta}=\sqrt{2404}=\sqrt{4*601}=\sqrt{4}*\sqrt{601}=2\sqrt{601}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{601}}{2*4}=\frac{66-2\sqrt{601}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{601}}{2*4}=\frac{66+2\sqrt{601}}{8}
$