60^2=(16a)^2+(9a)^2

Solution for 60^2=(16a)^2+(9a)^2 equation:

60^2=(16a)^2+(9a)^2

We move all terms to the left:

60^2-((16a)^2+(9a)^2)=0

We add all the numbers together, and all the variables

-(16a^2+9a^2)+3600=0

We get rid of parentheses

-16a^2-9a^2+3600=0

We add all the numbers together, and all the variables

-25a^2+3600=0

a = -25; b = 0; c = +3600;
Δ = b2-4ac
Δ = 02-4·(-25)·3600
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600}{2*-25}=\frac{-600}{-50}
=+12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600}{2*-25}=\frac{600}{-50}
=-12
$