7r^2=30-11r

Solution for 7r^2=30-11r equation:

7r^2=30-11r

We move all terms to the left:

7r^2-(30-11r)=0

We add all the numbers together, and all the variables

7r^2-(-11r+30)=0

We get rid of parentheses

7r^2+11r-30=0

a = 7; b = 11; c = -30;
Δ = b2-4ac
Δ = 112-4·7·(-30)
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{-(11)-31}{2*7}=\frac{-42}{14}
=-3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+31}{2*7}=\frac{20}{14}
=1+3/7
$