x^2=225/2

Solution for x^2=225/2 equation:

x^2=225/2

We move all terms to the left:

x^2-(225/2)=0

We add all the numbers together, and all the variables

x^2-(+225/2)=0

We get rid of parentheses

x^2-225/2=0

We multiply all the terms by the denominator


x^2*2-225=0

Wy multiply elements

2x^2-225=0

a = 2; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·2·(-225)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*2}=\frac{0-30\sqrt{2}}{4}
=-\frac{30\sqrt{2}}{4}
=-\frac{15\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*2}=\frac{0+30\sqrt{2}}{4}
=\frac{30\sqrt{2}}{4}
=\frac{15\sqrt{2}}{2}
$