30x^2-51x+9=0

Solution for 30x^2-51x+9=0 equation:

30x^2-51x+9=0

a = 30; b = -51; c = +9;
Δ = b2-4ac
Δ = -512-4·30·9
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-39}{2*30}=\frac{12}{60}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+39}{2*30}=\frac{90}{60}
=1+1/2
$