3/5m^2=3

Solution for 3/5m^2=3 equation:

3/5m^2=3

We move all terms to the left:

3/5m^2-(3)=0


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

m^2!=0/5

m^2!=√0

m!=0

m∈R


We multiply all the terms by the denominator


-3*5m^2+3=0

Wy multiply elements

-15m^2+3=0

a = -15; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-15)·3
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*-15}=\frac{0-6\sqrt{5}}{-30}
=-\frac{6\sqrt{5}}{-30}
=-\frac{\sqrt{5}}{-5}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*-15}=\frac{0+6\sqrt{5}}{-30}
=\frac{6\sqrt{5}}{-30}
=\frac{\sqrt{5}}{-5}
$