9=7/2x2+6

Solution for 9=7/2x2+6 equation:

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)!=0

x∈R


We get rid of parentheses

-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}
$