55^2=16x^2+9x^2

Solution for 55^2=16x^2+9x^2 equation:

55^2=16x^2+9x^2

We move all terms to the left:

55^2-(16x^2+9x^2)=0

We add all the numbers together, and all the variables

-(16x^2+9x^2)+3025=0

We get rid of parentheses

-16x^2-9x^2+3025=0

We add all the numbers together, and all the variables

-25x^2+3025=0

a = -25; b = 0; c = +3025;
Δ = b2-4ac
Δ = 02-4·(-25)·3025
Δ = 302500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{302500}=550$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-550}{2*-25}=\frac{-550}{-50}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+550}{2*-25}=\frac{550}{-50}
=-11
$