3r^2=5-r

Solution for 3r^2=5-r equation:

3r^2=5-r

We move all terms to the left:

3r^2-(5-r)=0

We add all the numbers together, and all the variables

3r^2-(-1r+5)=0

We get rid of parentheses

3r^2+1r-5=0

We add all the numbers together, and all the variables

3r^2+r-5=0

a = 3; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·3·(-5)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{61}}{2*3}=\frac{-1-\sqrt{61}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{61}}{2*3}=\frac{-1+\sqrt{61}}{6}
$