25/16x^2=125

Solution for 25/16x^2=125 equation:

25/16x^2=125

We move all terms to the left:

25/16x^2-(125)=0


Domain of the equation: 16x^2!=0

x^2!=0/16

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-125*16x^2+25=0

Wy multiply elements

-2000x^2+25=0

a = -2000; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-2000)·25
Δ = 200000
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:

$\sqrt{\Delta}=\sqrt{200000}=\sqrt{40000*5}=\sqrt{40000}*\sqrt{5}=200\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{5}}{2*-2000}=\frac{0-200\sqrt{5}}{-4000}
=-\frac{200\sqrt{5}}{-4000}
=-\frac{\sqrt{5}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{5}}{2*-2000}=\frac{0+200\sqrt{5}}{-4000}
=\frac{200\sqrt{5}}{-4000}
=\frac{\sqrt{5}}{-20}
$