x2-72x+160=0

Solution for x2-72x+160=0 equation:

x2-72x+160=0

We add all the numbers together, and all the variables

x^2-72x+160=0

a = 1; b = -72; c = +160;
Δ = b2-4ac
Δ = -722-4·1·160
Δ = 4544
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:

$\sqrt{\Delta}=\sqrt{4544}=\sqrt{64*71}=\sqrt{64}*\sqrt{71}=8\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{71}}{2*1}=\frac{72-8\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{71}}{2*1}=\frac{72+8\sqrt{71}}{2}
$