40x^2+90x+27=0

Solution for 40x^2+90x+27=0 equation:

40x^2+90x+27=0

a = 40; b = 90; c = +27;
Δ = b2-4ac
Δ = 902-4·40·27
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{105}}{2*40}=\frac{-90-6\sqrt{105}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{105}}{2*40}=\frac{-90+6\sqrt{105}}{80}
$