3r^2=2-10r

Solution for 3r^2=2-10r equation:

3r^2=2-10r

We move all terms to the left:

3r^2-(2-10r)=0

We add all the numbers together, and all the variables

3r^2-(-10r+2)=0

We get rid of parentheses

3r^2+10r-2=0

a = 3; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·3·(-2)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{31}}{2*3}=\frac{-10-2\sqrt{31}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{31}}{2*3}=\frac{-10+2\sqrt{31}}{6}
$