y^2=429/49

Solution for y^2=429/49 equation:

y^2=429/49

We move all terms to the left:

y^2-(429/49)=0

We add all the numbers together, and all the variables

y^2-(+429/49)=0

We get rid of parentheses

y^2-429/49=0

We multiply all the terms by the denominator


y^2*49-429=0

Wy multiply elements

49y^2-429=0

a = 49; b = 0; c = -429;
Δ = b2-4ac
Δ = 02-4·49·(-429)
Δ = 84084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84084}=\sqrt{196*429}=\sqrt{196}*\sqrt{429}=14\sqrt{429}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{429}}{2*49}=\frac{0-14\sqrt{429}}{98}
=-\frac{14\sqrt{429}}{98}
=-\frac{\sqrt{429}}{7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{429}}{2*49}=\frac{0+14\sqrt{429}}{98}
=\frac{14\sqrt{429}}{98}
=\frac{\sqrt{429}}{7}
$