144x2-324x-80=0

Solution for 144x2-324x-80=0 equation:

144x^2-324x-80=0

a = 144; b = -324; c = -80;
Δ = b2-4ac
Δ = -3242-4·144·(-80)
Δ = 151056
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:

$\sqrt{\Delta}=\sqrt{151056}=\sqrt{144*1049}=\sqrt{144}*\sqrt{1049}=12\sqrt{1049}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-12\sqrt{1049}}{2*144}=\frac{324-12\sqrt{1049}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+12\sqrt{1049}}{2*144}=\frac{324+12\sqrt{1049}}{288}
$