1/7x^2+4=11

Solution for 1/7x^2+4=11 equation:

1/7x^2+4=11

We move all terms to the left:

1/7x^2+4-(11)=0


Domain of the equation: 7x^2!=0

x^2!=0/7

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

1/7x^2-7=0

We multiply all the terms by the denominator


-7*7x^2+1=0

Wy multiply elements

-49x^2+1=0

a = -49; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-49)·1
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*-49}=\frac{-14}{-98}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*-49}=\frac{14}{-98}
=-1/7
$