39-14r^2+7(21-5r^2)+30r^2=0

Solution for 39-14r^2+7(21-5r^2)+30r^2=0 equation:

39-14r^2+7(21-5r^2)+30r^2=0

We add all the numbers together, and all the variables

16r^2+7(21-5r^2)+39=0

We multiply parentheses

16r^2-35r^2+147+39=0

We add all the numbers together, and all the variables

-19r^2+186=0

a = -19; b = 0; c = +186;
Δ = b2-4ac
Δ = 02-4·(-19)·186
Δ = 14136
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:

$\sqrt{\Delta}=\sqrt{14136}=\sqrt{4*3534}=\sqrt{4}*\sqrt{3534}=2\sqrt{3534}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3534}}{2*-19}=\frac{0-2\sqrt{3534}}{-38}
=-\frac{2\sqrt{3534}}{-38}
=-\frac{\sqrt{3534}}{-19}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3534}}{2*-19}=\frac{0+2\sqrt{3534}}{-38}
=\frac{2\sqrt{3534}}{-38}
=\frac{\sqrt{3534}}{-19}
$