x^2-144x+320=0

Solution for x^2-144x+320=0 equation:

x^2-144x+320=0

a = 1; b = -144; c = +320;
Δ = b2-4ac
Δ = -1442-4·1·320
Δ = 19456
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:

$\sqrt{\Delta}=\sqrt{19456}=\sqrt{1024*19}=\sqrt{1024}*\sqrt{19}=32\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-32\sqrt{19}}{2*1}=\frac{144-32\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+32\sqrt{19}}{2*1}=\frac{144+32\sqrt{19}}{2}
$