7r^2+3=192

Solution for 7r^2+3=192 equation:

7r^2+3=192

We move all terms to the left:

7r^2+3-(192)=0

We add all the numbers together, and all the variables

7r^2-189=0

a = 7; b = 0; c = -189;
Δ = b2-4ac
Δ = 02-4·7·(-189)
Δ = 5292
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:

$\sqrt{\Delta}=\sqrt{5292}=\sqrt{1764*3}=\sqrt{1764}*\sqrt{3}=42\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42\sqrt{3}}{2*7}=\frac{0-42\sqrt{3}}{14}
=-\frac{42\sqrt{3}}{14}
=-3\sqrt{3}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42\sqrt{3}}{2*7}=\frac{0+42\sqrt{3}}{14}
=\frac{42\sqrt{3}}{14}
=3\sqrt{3}
$