x*x+17=84

Solution for x*x+17=84 equation:

x*x+17=84

We move all terms to the left:

x*x+17-(84)=0

We add all the numbers together, and all the variables

x*x-67=0

Wy multiply elements

x^2-67=0

a = 1; b = 0; c = -67;
Δ = b2-4ac
Δ = 02-4·1·(-67)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{67}}{2*1}=\frac{0-2\sqrt{67}}{2}
=-\frac{2\sqrt{67}}{2}
=-\sqrt{67}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{67}}{2*1}=\frac{0+2\sqrt{67}}{2}
=\frac{2\sqrt{67}}{2}
=\sqrt{67}
$