5r2-44r+120=-30+11r

Solution for 5r2-44r+120=-30+11r equation:

5r^2-44r+120=-30+11r

We move all terms to the left:

5r^2-44r+120-(-30+11r)=0

We add all the numbers together, and all the variables

5r^2-44r-(11r-30)+120=0

We get rid of parentheses

5r^2-44r-11r+30+120=0

We add all the numbers together, and all the variables

5r^2-55r+150=0

a = 5; b = -55; c = +150;
Δ = b2-4ac
Δ = -552-4·5·150
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5}{2*5}=\frac{50}{10}
=5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5}{2*5}=\frac{60}{10}
=6
$