49r^2=147

Solution for 49r^2=147 equation:

49r^2=147

We move all terms to the left:

49r^2-(147)=0

a = 49; b = 0; c = -147;
Δ = b2-4ac
Δ = 02-4·49·(-147)
Δ = 28812
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:

$\sqrt{\Delta}=\sqrt{28812}=\sqrt{9604*3}=\sqrt{9604}*\sqrt{3}=98\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-98\sqrt{3}}{2*49}=\frac{0-98\sqrt{3}}{98}
=-\frac{98\sqrt{3}}{98}
=-\sqrt{3}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+98\sqrt{3}}{2*49}=\frac{0+98\sqrt{3}}{98}
=\frac{98\sqrt{3}}{98}
=\sqrt{3}
$