5=97/11x2

Solution for 5=97/11x2 equation:

5=97/11x^2

We move all terms to the left:

5-(97/11x^2)=0


Domain of the equation: 11x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-97/11x^2+5=0

We multiply all the terms by the denominator


5*11x^2-97=0

Wy multiply elements

55x^2-97=0

a = 55; b = 0; c = -97;
Δ = b2-4ac
Δ = 02-4·55·(-97)
Δ = 21340
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:

$\sqrt{\Delta}=\sqrt{21340}=\sqrt{4*5335}=\sqrt{4}*\sqrt{5335}=2\sqrt{5335}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5335}}{2*55}=\frac{0-2\sqrt{5335}}{110}
=-\frac{2\sqrt{5335}}{110}
=-\frac{\sqrt{5335}}{55}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5335}}{2*55}=\frac{0+2\sqrt{5335}}{110}
=\frac{2\sqrt{5335}}{110}
=\frac{\sqrt{5335}}{55}
$