4r^2+9r=9

Solution for 4r^2+9r=9 equation:

4r^2+9r=9

We move all terms to the left:

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

a = 4; b = 9; c = -9;
Δ = b2-4ac
Δ = 92-4·4·(-9)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*4}=\frac{-24}{8}
=-3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*4}=\frac{6}{8}
=3/4
$