2r^2-3=611

Solution for 2r^2-3=611 equation:

2r^2-3=611

We move all terms to the left:

2r^2-3-(611)=0

We add all the numbers together, and all the variables

2r^2-614=0

a = 2; b = 0; c = -614;
Δ = b2-4ac
Δ = 02-4·2·(-614)
Δ = 4912
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:

$\sqrt{\Delta}=\sqrt{4912}=\sqrt{16*307}=\sqrt{16}*\sqrt{307}=4\sqrt{307}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{307}}{2*2}=\frac{0-4\sqrt{307}}{4}
=-\frac{4\sqrt{307}}{4}
=-\sqrt{307}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{307}}{2*2}=\frac{0+4\sqrt{307}}{4}
=\frac{4\sqrt{307}}{4}
=\sqrt{307}
$