9r=4r^2-28

Solution for 9r=4r^2-28 equation:

9r=4r^2-28

We move all terms to the left:

9r-(4r^2-28)=0

We get rid of parentheses

-4r^2+9r+28=0

a = -4; b = 9; c = +28;
Δ = b2-4ac
Δ = 92-4·(-4)·28
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-23}{2*-4}=\frac{-32}{-8}
=+4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+23}{2*-4}=\frac{14}{-8}
=-1+3/4
$