x^2=74.25

Solution for x^2=74.25 equation:

x^2=74.25

We move all terms to the left:

x^2-(74.25)=0

We add all the numbers together, and all the variables

x^2-74.25=0

a = 1; b = 0; c = -74.25;
Δ = b2-4ac
Δ = 02-4·1·(-74.25)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{33}}{2*1}=\frac{0-3\sqrt{33}}{2}
=-\frac{3\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{33}}{2*1}=\frac{0+3\sqrt{33}}{2}
=\frac{3\sqrt{33}}{2}
$