25+x^2+8x^2=100

Solution for 25+x^2+8x^2=100 equation:

25+x^2+8x^2=100

We move all terms to the left:

25+x^2+8x^2-(100)=0

We add all the numbers together, and all the variables

9x^2-75=0

a = 9; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·9·(-75)
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{3}}{2*9}=\frac{0-30\sqrt{3}}{18}
=-\frac{30\sqrt{3}}{18}
=-\frac{5\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{3}}{2*9}=\frac{0+30\sqrt{3}}{18}
=\frac{30\sqrt{3}}{18}
=\frac{5\sqrt{3}}{3}
$