8r2-17=2471

Solution for 8r2-17=2471 equation:

8r^2-17=2471

We move all terms to the left:

8r^2-17-(2471)=0

We add all the numbers together, and all the variables

8r^2-2488=0

a = 8; b = 0; c = -2488;
Δ = b2-4ac
Δ = 02-4·8·(-2488)
Δ = 79616
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:

$\sqrt{\Delta}=\sqrt{79616}=\sqrt{256*311}=\sqrt{256}*\sqrt{311}=16\sqrt{311}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{311}}{2*8}=\frac{0-16\sqrt{311}}{16}
=-\frac{16\sqrt{311}}{16}
=-\sqrt{311}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{311}}{2*8}=\frac{0+16\sqrt{311}}{16}
=\frac{16\sqrt{311}}{16}
=\sqrt{311}
$