X^2+(x^2/16)=36

Solution for X^2+(x^2/16)=36 equation:

X^2+(X^2/16)=36

We move all terms to the left:

X^2+(X^2/16)-(36)=0

We get rid of parentheses

X^2+X^2/16-36=0

We multiply all the terms by the denominator


X^2+X^2*16-36*16=0

We add all the numbers together, and all the variables

X^2+X^2*16-576=0

Wy multiply elements

X^2+16X^2-576=0

We add all the numbers together, and all the variables

17X^2-576=0

a = 17; b = 0; c = -576;
Δ = b2-4ac
Δ = 02-4·17·(-576)
Δ = 39168
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:

$\sqrt{\Delta}=\sqrt{39168}=\sqrt{2304*17}=\sqrt{2304}*\sqrt{17}=48\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{17}}{2*17}=\frac{0-48\sqrt{17}}{34}
=-\frac{48\sqrt{17}}{34}
=-\frac{24\sqrt{17}}{17}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{17}}{2*17}=\frac{0+48\sqrt{17}}{34}
=\frac{48\sqrt{17}}{34}
=\frac{24\sqrt{17}}{17}
$