7r^2=259

Solution for 7r^2=259 equation:

7r^2=259

We move all terms to the left:

7r^2-(259)=0

a = 7; b = 0; c = -259;
Δ = b2-4ac
Δ = 02-4·7·(-259)
Δ = 7252
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:

$\sqrt{\Delta}=\sqrt{7252}=\sqrt{196*37}=\sqrt{196}*\sqrt{37}=14\sqrt{37}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{37}}{2*7}=\frac{0-14\sqrt{37}}{14}
=-\frac{14\sqrt{37}}{14}
=-\sqrt{37}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{37}}{2*7}=\frac{0+14\sqrt{37}}{14}
=\frac{14\sqrt{37}}{14}
=\sqrt{37}
$