27x^2+75X+20=0

Solution for 27x^2+75X+20=0 equation:

27x^2+75x+20=0

a = 27; b = 75; c = +20;
Δ = b2-4ac
Δ = 752-4·27·20
Δ = 3465
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:

$\sqrt{\Delta}=\sqrt{3465}=\sqrt{9*385}=\sqrt{9}*\sqrt{385}=3\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-3\sqrt{385}}{2*27}=\frac{-75-3\sqrt{385}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+3\sqrt{385}}{2*27}=\frac{-75+3\sqrt{385}}{54}
$