x^2=400/169

Solution for x^2=400/169 equation:

x^2=400/169

We move all terms to the left:

x^2-(400/169)=0

We add all the numbers together, and all the variables

x^2-(+400/169)=0

We get rid of parentheses

x^2-400/169=0

We multiply all the terms by the denominator


x^2*169-400=0

Wy multiply elements

169x^2-400=0

a = 169; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·169·(-400)
Δ = 270400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{270400}=520$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-520}{2*169}=\frac{-520}{338}
=-1+7/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+520}{2*169}=\frac{520}{338}
=1+7/13
$