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9=7/2x^2+6
We move all terms to the left:
9-(7/2x^2+6)=0
Domain of the equation: 2x^2+6)!=0We get rid of parentheses
x∈R
-7/2x^2-6+9=0
We multiply all the terms by the denominator
-6*2x^2+9*2x^2-7=0
Wy multiply elements
-12x^2+18x^2-7=0
We add all the numbers together, and all the variables
6x^2-7=0
a = 6; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·6·(-7)
Δ = 168
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*6}=\frac{0-2\sqrt{42}}{12} =-\frac{2\sqrt{42}}{12} =-\frac{\sqrt{42}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*6}=\frac{0+2\sqrt{42}}{12} =\frac{2\sqrt{42}}{12} =\frac{\sqrt{42}}{6} $
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