36/25x^2=6

Solution for 36/25x^2=6 equation:

36/25x^2=6

We move all terms to the left:

36/25x^2-(6)=0


Domain of the equation: 25x^2!=0

x^2!=0/25

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-6*25x^2+36=0

Wy multiply elements

-150x^2+36=0

a = -150; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-150)·36
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{6}}{2*-150}=\frac{0-60\sqrt{6}}{-300}
=-\frac{60\sqrt{6}}{-300}
=-\frac{\sqrt{6}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{6}}{2*-150}=\frac{0+60\sqrt{6}}{-300}
=\frac{60\sqrt{6}}{-300}
=\frac{\sqrt{6}}{-5}
$