171*x*x=72

Solution for 171*x*x=72 equation:

171x*x=72

We move all terms to the left:

171x*x-(72)=0

Wy multiply elements

171x^2-72=0

a = 171; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·171·(-72)
Δ = 49248
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:

$\sqrt{\Delta}=\sqrt{49248}=\sqrt{1296*38}=\sqrt{1296}*\sqrt{38}=36\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{38}}{2*171}=\frac{0-36\sqrt{38}}{342}
=-\frac{36\sqrt{38}}{342}
=-\frac{2\sqrt{38}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{38}}{2*171}=\frac{0+36\sqrt{38}}{342}
=\frac{36\sqrt{38}}{342}
=\frac{2\sqrt{38}}{19}
$