16X^2+5y^2=90

Solution for 16X^2+5y^2=90 equation:

16X^2+5X^2=90

We move all terms to the left:

16X^2+5X^2-(90)=0

We add all the numbers together, and all the variables

21X^2-90=0

a = 21; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·21·(-90)
Δ = 7560
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:

$\sqrt{\Delta}=\sqrt{7560}=\sqrt{36*210}=\sqrt{36}*\sqrt{210}=6\sqrt{210}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{210}}{2*21}=\frac{0-6\sqrt{210}}{42}
=-\frac{6\sqrt{210}}{42}
=-\frac{\sqrt{210}}{7}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{210}}{2*21}=\frac{0+6\sqrt{210}}{42}
=\frac{6\sqrt{210}}{42}
=\frac{\sqrt{210}}{7}
$