x2-61=160

Solution for x2-61=160 equation:

x2-61=160

We move all terms to the left:

x2-61-(160)=0

We add all the numbers together, and all the variables

x^2-221=0

a = 1; b = 0; c = -221;
Δ = b2-4ac
Δ = 02-4·1·(-221)
Δ = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{221}}{2*1}=\frac{0-2\sqrt{221}}{2}
=-\frac{2\sqrt{221}}{2}
=-\sqrt{221}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{221}}{2*1}=\frac{0+2\sqrt{221}}{2}
=\frac{2\sqrt{221}}{2}
=\sqrt{221}
$