x^2+11/2=7

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Solution for x^2+11/2=7 equation: 



x^2+11/2=7

We move all terms to the left:

x^2+11/2-(7)=0

determiningTheFunctionDomain
x^2-7+11/2=0

We multiply all the terms by the denominator


x^2*2+11-7*2=0

We add all the numbers together, and all the variables

x^2*2-3=0

Wy multiply elements

2x^2-3=0

a = 2; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·2·(-3)
Δ = 24
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:


$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*2}=\frac{0-2\sqrt{6}}{4}
=-\frac{2\sqrt{6}}{4}
=-\frac{\sqrt{6}}{2}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*2}=\frac{0+2\sqrt{6}}{4}
=\frac{2\sqrt{6}}{4}
=\frac{\sqrt{6}}{2}
$

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