144x^2-408x+64=0

Solution for 144x^2-408x+64=0 equation:

144x^2-408x+64=0

a = 144; b = -408; c = +64;
Δ = b2-4ac
Δ = -4082-4·144·64
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-408)-360}{2*144}=\frac{48}{288}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-408)+360}{2*144}=\frac{768}{288}
=2+2/3
$