x^2=100/169

Solution for x^2=100/169 equation:

x^2=100/169

We move all terms to the left:

x^2-(100/169)=0

We add all the numbers together, and all the variables

x^2-(+100/169)=0

We get rid of parentheses

x^2-100/169=0

We multiply all the terms by the denominator


x^2*169-100=0

Wy multiply elements

169x^2-100=0

a = 169; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·169·(-100)
Δ = 67600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67600}=260$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-260}{2*169}=\frac{-260}{338}
=-10/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+260}{2*169}=\frac{260}{338}
=10/13
$