9x^2-9=40-x^2

Solution for 9x^2-9=40-x^2 equation:

9x^2-9=40-x^2

We move all terms to the left:

9x^2-9-(40-x^2)=0

We get rid of parentheses

9x^2+x^2-40-9=0

We add all the numbers together, and all the variables

10x^2-49=0

a = 10; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·10·(-49)
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{10}}{2*10}=\frac{0-14\sqrt{10}}{20}
=-\frac{14\sqrt{10}}{20}
=-\frac{7\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{10}}{2*10}=\frac{0+14\sqrt{10}}{20}
=\frac{14\sqrt{10}}{20}
=\frac{7\sqrt{10}}{10}
$