x^2-11/7=10

Solution for x^2-11/7=10 equation:

x^2-11/7=10

We move all terms to the left:

x^2-11/7-(10)=0

determiningTheFunctionDomain
x^2-10-11/7=0

We multiply all the terms by the denominator


x^2*7-11-10*7=0

We add all the numbers together, and all the variables

x^2*7-81=0

Wy multiply elements

7x^2-81=0

a = 7; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·7·(-81)
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{7}}{2*7}=\frac{0-18\sqrt{7}}{14}
=-\frac{18\sqrt{7}}{14}
=-\frac{9\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{7}}{2*7}=\frac{0+18\sqrt{7}}{14}
=\frac{18\sqrt{7}}{14}
=\frac{9\sqrt{7}}{7}
$