x^2-5/2=58

Solution for x^2-5/2=58 equation:

x^2-5/2=58

We move all terms to the left:

x^2-5/2-(58)=0

determiningTheFunctionDomain
x^2-58-5/2=0

We multiply all the terms by the denominator


x^2*2-5-58*2=0

We add all the numbers together, and all the variables

x^2*2-121=0

Wy multiply elements

2x^2-121=0

a = 2; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·2·(-121)
Δ = 968
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:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{2}}{2*2}=\frac{0-22\sqrt{2}}{4}
=-\frac{22\sqrt{2}}{4}
=-\frac{11\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{2}}{2*2}=\frac{0+22\sqrt{2}}{4}
=\frac{22\sqrt{2}}{4}
=\frac{11\sqrt{2}}{2}
$