6r^2-9r+4/3=0

Solution for 6r^2-9r+4/3=0 equation:

6r^2-9r+4/3=0

We multiply all the terms by the denominator


6r^2*3-9r*3+4=0

Wy multiply elements

18r^2-27r+4=0

a = 18; b = -27; c = +4;
Δ = b2-4ac
Δ = -272-4·18·4
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-21}{2*18}=\frac{6}{36}
=1/6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+21}{2*18}=\frac{48}{36}
=1+1/3
$