3x^2-45x+27=0

Solution for 3x^2-45x+27=0 equation:

3x^2-45x+27=0

a = 3; b = -45; c = +27;
Δ = b2-4ac
Δ = -452-4·3·27
Δ = 1701
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1701}=\sqrt{81*21}=\sqrt{81}*\sqrt{21}=9\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-9\sqrt{21}}{2*3}=\frac{45-9\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+9\sqrt{21}}{2*3}=\frac{45+9\sqrt{21}}{6}
$