1/2(25x2)-125=0

Solution for 1/2(25x2)-125=0 equation:

1/2(25x^2)-125=0


Domain of the equation: 225x^2!=0

x^2!=0/225

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-125*225x^2+1=0

Wy multiply elements

-28125x^2+1=0

a = -28125; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-28125)·1
Δ = 112500
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:

$\sqrt{\Delta}=\sqrt{112500}=\sqrt{22500*5}=\sqrt{22500}*\sqrt{5}=150\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150\sqrt{5}}{2*-28125}=\frac{0-150\sqrt{5}}{-56250}
=-\frac{150\sqrt{5}}{-56250}
=-\frac{\sqrt{5}}{-375}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150\sqrt{5}}{2*-28125}=\frac{0+150\sqrt{5}}{-56250}
=\frac{150\sqrt{5}}{-56250}
=\frac{\sqrt{5}}{-375}
$