8/5x2=25

Solution for 8/5x2=25 equation:

8/5x^2=25

We move all terms to the left:

8/5x^2-(25)=0


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

x^2!=0/5

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-25*5x^2+8=0

Wy multiply elements

-125x^2+8=0

a = -125; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-125)·8
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{10}}{2*-125}=\frac{0-20\sqrt{10}}{-250}
=-\frac{20\sqrt{10}}{-250}
=-\frac{2\sqrt{10}}{-25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{10}}{2*-125}=\frac{0+20\sqrt{10}}{-250}
=\frac{20\sqrt{10}}{-250}
=\frac{2\sqrt{10}}{-25}
$