r^2+2r=24+3r

Solution for r^2+2r=24+3r equation:

r^2+2r=24+3r

We move all terms to the left:

r^2+2r-(24+3r)=0

We add all the numbers together, and all the variables

r^2+2r-(3r+24)=0

We get rid of parentheses

r^2+2r-3r-24=0

We add all the numbers together, and all the variables

r^2-1r-24=0

a = 1; b = -1; c = -24;
Δ = b2-4ac
Δ = -12-4·1·(-24)
Δ = 97
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{97}}{2*1}=\frac{1-\sqrt{97}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*1}=\frac{1+\sqrt{97}}{2}
$