r^2=77/49

Solution for r^2=77/49 equation:

r^2=77/49

We move all terms to the left:

r^2-(77/49)=0

We add all the numbers together, and all the variables

r^2-(+77/49)=0

We get rid of parentheses

r^2-77/49=0

We multiply all the terms by the denominator


r^2*49-77=0

Wy multiply elements

49r^2-77=0

a = 49; b = 0; c = -77;
Δ = b2-4ac
Δ = 02-4·49·(-77)
Δ = 15092
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15092}=\sqrt{196*77}=\sqrt{196}*\sqrt{77}=14\sqrt{77}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{77}}{2*49}=\frac{0-14\sqrt{77}}{98}
=-\frac{14\sqrt{77}}{98}
=-\frac{\sqrt{77}}{7}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{77}}{2*49}=\frac{0+14\sqrt{77}}{98}
=\frac{14\sqrt{77}}{98}
=\frac{\sqrt{77}}{7}
$