2x^2-5=41/2

Solution for 2x^2-5=41/2 equation:

2x^2-5=41/2

We move all terms to the left:

2x^2-5-(41/2)=0

We add all the numbers together, and all the variables

2x^2-5-(+41/2)=0

We get rid of parentheses

2x^2-5-41/2=0

We multiply all the terms by the denominator


2x^2*2-41-5*2=0

We add all the numbers together, and all the variables

2x^2*2-51=0

Wy multiply elements

4x^2-51=0

a = 4; b = 0; c = -51;
Δ = b2-4ac
Δ = 02-4·4·(-51)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{51}}{2*4}=\frac{0-4\sqrt{51}}{8}
=-\frac{4\sqrt{51}}{8}
=-\frac{\sqrt{51}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{51}}{2*4}=\frac{0+4\sqrt{51}}{8}
=\frac{4\sqrt{51}}{8}
=\frac{\sqrt{51}}{2}
$