3-7r^2=-39

Solution for 3-7r^2=-39 equation:

3-7r^2=-39

We move all terms to the left:

3-7r^2-(-39)=0

We add all the numbers together, and all the variables

-7r^2+42=0

a = -7; b = 0; c = +42;
Δ = b2-4ac
Δ = 02-4·(-7)·42
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{6}}{2*-7}=\frac{0-14\sqrt{6}}{-14}
=-\frac{14\sqrt{6}}{-14}
=-\frac{\sqrt{6}}{-1}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{6}}{2*-7}=\frac{0+14\sqrt{6}}{-14}
=\frac{14\sqrt{6}}{-14}
=\frac{\sqrt{6}}{-1}
$