9x^2+16x^2=100

Solution for 9x^2+16x^2=100 equation:

9x^2+16x^2=100

We move all terms to the left:

9x^2+16x^2-(100)=0

We add all the numbers together, and all the variables

25x^2-100=0

a = 25; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·25·(-100)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*25}=\frac{-100}{50}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*25}=\frac{100}{50}
=2
$