3r^2=76+7r

Solution for 3r^2=76+7r equation:

3r^2=76+7r

We move all terms to the left:

3r^2-(76+7r)=0

We add all the numbers together, and all the variables

3r^2-(7r+76)=0

We get rid of parentheses

3r^2-7r-76=0

a = 3; b = -7; c = -76;
Δ = b2-4ac
Δ = -72-4·3·(-76)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-31}{2*3}=\frac{-24}{6}
=-4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+31}{2*3}=\frac{38}{6}
=6+1/3
$