4/5x^2-1=7

Solution for 4/5x^2-1=7 equation:

4/5x^2-1=7

We move all terms to the left:

4/5x^2-1-(7)=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

4/5x^2-8=0

We multiply all the terms by the denominator


-8*5x^2+4=0

Wy multiply elements

-40x^2+4=0

a = -40; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-40)·4
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-40}=\frac{0-8\sqrt{10}}{-80}
=-\frac{8\sqrt{10}}{-80}
=-\frac{\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-40}=\frac{0+8\sqrt{10}}{-80}
=\frac{8\sqrt{10}}{-80}
=\frac{\sqrt{10}}{-10}
$