3/5x^2-12=9

Solution for 3/5x^2-12=9 equation:

3/5x^2-12=9

We move all terms to the left:

3/5x^2-12-(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

3/5x^2-21=0

We multiply all the terms by the denominator


-21*5x^2+3=0

Wy multiply elements

-105x^2+3=0

a = -105; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-105)·3
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{35}}{2*-105}=\frac{0-6\sqrt{35}}{-210}
=-\frac{6\sqrt{35}}{-210}
=-\frac{\sqrt{35}}{-35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{35}}{2*-105}=\frac{0+6\sqrt{35}}{-210}
=\frac{6\sqrt{35}}{-210}
=\frac{\sqrt{35}}{-35}
$