-6/5x^2=-5

Solution for -6/5x^2=-5 equation:

-6/5x^2=-5

We move all terms to the left:

-6/5x^2-(-5)=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

-6/5x^2+5=0

We multiply all the terms by the denominator


5*5x^2-6=0

Wy multiply elements

25x^2-6=0

a = 25; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·25·(-6)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*25}=\frac{0-10\sqrt{6}}{50}
=-\frac{10\sqrt{6}}{50}
=-\frac{\sqrt{6}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*25}=\frac{0+10\sqrt{6}}{50}
=\frac{10\sqrt{6}}{50}
=\frac{\sqrt{6}}{5}
$