x^2=100/15

Solution for x^2=100/15 equation:

x^2=100/15

We move all terms to the left:

x^2-(100/15)=0

We add all the numbers together, and all the variables

x^2-(+100/15)=0

We get rid of parentheses

x^2-100/15=0

We multiply all the terms by the denominator


x^2*15-100=0

Wy multiply elements

15x^2-100=0

a = 15; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·15·(-100)
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{15}}{2*15}=\frac{0-20\sqrt{15}}{30}
=-\frac{20\sqrt{15}}{30}
=-\frac{2\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{15}}{2*15}=\frac{0+20\sqrt{15}}{30}
=\frac{20\sqrt{15}}{30}
=\frac{2\sqrt{15}}{3}
$