16-(1)/(5)x^2=9

Solution for 16-(1)/(5)x^2=9 equation:

16-(1)/(5)x^2=9

We move all terms to the left:

16-(1)/(5)x^2-(9)=0


Domain of the equation: 5x^2!=0

x^2!=0/5

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

-1/5x^2+7=0

We multiply all the terms by the denominator


7*5x^2-1=0

Wy multiply elements

35x^2-1=0

a = 35; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·35·(-1)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35}}{2*35}=\frac{0-2\sqrt{35}}{70}
=-\frac{2\sqrt{35}}{70}
=-\frac{\sqrt{35}}{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*35}=\frac{0+2\sqrt{35}}{70}
=\frac{2\sqrt{35}}{70}
=\frac{\sqrt{35}}{35}
$