18x^2-51x+21=0

Solution for 18x^2-51x+21=0 equation:

18x^2-51x+21=0

a = 18; b = -51; c = +21;
Δ = b2-4ac
Δ = -512-4·18·21
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-33}{2*18}=\frac{18}{36}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+33}{2*18}=\frac{84}{36}
=2+1/3
$