4r^2-9=11r

Solution for 4r^2-9=11r equation:

4r^2-9=11r

We move all terms to the left:

4r^2-9-(11r)=0

a = 4; b = -11; c = -9;
Δ = b2-4ac
Δ = -112-4·4·(-9)
Δ = 265
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{-(-11)-\sqrt{265}}{2*4}=\frac{11-\sqrt{265}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{265}}{2*4}=\frac{11+\sqrt{265}}{8}
$