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 = 12420
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:

$\sqrt{\Delta}=\sqrt{12420}=\sqrt{36*345}=\sqrt{36}*\sqrt{345}=6\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{345}}{2*40}=\frac{90-6\sqrt{345}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{345}}{2*40}=\frac{90+6\sqrt{345}}{80}
$