27x^2+81x+45=0

Solution for 27x^2+81x+45=0 equation:

27x^2+81x+45=0

a = 27; b = 81; c = +45;
Δ = b2-4ac
Δ = 812-4·27·45
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{-(81)-9\sqrt{21}}{2*27}=\frac{-81-9\sqrt{21}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+9\sqrt{21}}{2*27}=\frac{-81+9\sqrt{21}}{54}
$