4/5x2=100

Solution for 4/5x2=100 equation:

4/5x^2=100

We move all terms to the left:

4/5x^2-(100)=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


-100*5x^2+4=0

Wy multiply elements

-500x^2+4=0

a = -500; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-500)·4
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*-500}=\frac{0-40\sqrt{5}}{-1000}
=-\frac{40\sqrt{5}}{-1000}
=-\frac{\sqrt{5}}{-25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*-500}=\frac{0+40\sqrt{5}}{-1000}
=\frac{40\sqrt{5}}{-1000}
=\frac{\sqrt{5}}{-25}
$