70-6/5*x^2=7/5*x^2+4

Solution for 70-6/5*x^2=7/5*x^2+4 equation:

70-6/5x^2=7/5x^2+4

We move all terms to the left:

70-6/5x^2-(7/5x^2+4)=0


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

x^2!=0/5

x^2!=√0

x!=0

x∈R



Domain of the equation: 5x^2+4)!=0

x∈R


We get rid of parentheses

-6/5x^2-7/5x^2-4+70=0

We multiply all the terms by the denominator


-4*5x^2+70*5x^2-6-7=0

We add all the numbers together, and all the variables

-4*5x^2+70*5x^2-13=0

Wy multiply elements

-20x^2+350x^2-13=0

We add all the numbers together, and all the variables

330x^2-13=0

a = 330; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·330·(-13)
Δ = 17160
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:

$\sqrt{\Delta}=\sqrt{17160}=\sqrt{4*4290}=\sqrt{4}*\sqrt{4290}=2\sqrt{4290}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{4290}}{2*330}=\frac{0-2\sqrt{4290}}{660}
=-\frac{2\sqrt{4290}}{660}
=-\frac{\sqrt{4290}}{330}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{4290}}{2*330}=\frac{0+2\sqrt{4290}}{660}
=\frac{2\sqrt{4290}}{660}
=\frac{\sqrt{4290}}{330}
$