6x^2+45x+45=0

Solution for 6x^2+45x+45=0 equation:

6x^2+45x+45=0

a = 6; b = 45; c = +45;
Δ = b2-4ac
Δ = 452-4·6·45
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{105}}{2*6}=\frac{-45-3\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{105}}{2*6}=\frac{-45+3\sqrt{105}}{12}
$