5-5r^2=-265

Solution for 5-5r^2=-265 equation:

5-5r^2=-265

We move all terms to the left:

5-5r^2-(-265)=0

We add all the numbers together, and all the variables

-5r^2+270=0

a = -5; b = 0; c = +270;
Δ = b2-4ac
Δ = 02-4·(-5)·270
Δ = 5400
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:

$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{6}}{2*-5}=\frac{0-30\sqrt{6}}{-10}
=-\frac{30\sqrt{6}}{-10}
=-\frac{3\sqrt{6}}{-1}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{6}}{2*-5}=\frac{0+30\sqrt{6}}{-10}
=\frac{30\sqrt{6}}{-10}
=\frac{3\sqrt{6}}{-1}
$