99x^2-9=40-x^2=0

Solution for 99x^2-9=40-x^2=0 equation:

99x^2-9=40-x^2=0

We move all terms to the left:

99x^2-9-(40-x^2)=0

We get rid of parentheses

99x^2+x^2-40-9=0

We add all the numbers together, and all the variables

100x^2-49=0

a = 100; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·100·(-49)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-140}{2*100}=\frac{-140}{200}
=-7/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+140}{2*100}=\frac{140}{200}
=7/10
$