9x^2+16x^2=27

Solution for 9x^2+16x^2=27 equation:

9x^2+16x^2=27

We move all terms to the left:

9x^2+16x^2-(27)=0

We add all the numbers together, and all the variables

25x^2-27=0

a = 25; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·25·(-27)
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*25}=\frac{0-30\sqrt{3}}{50}
=-\frac{30\sqrt{3}}{50}
=-\frac{3\sqrt{3}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{3}}{2*25}=\frac{0+30\sqrt{3}}{50}
=\frac{30\sqrt{3}}{50}
=\frac{3\sqrt{3}}{5}
$