27x^2+460x+48=0

Solution for 27x^2+460x+48=0 equation:

27x^2+460x+48=0

a = 27; b = 460; c = +48;
Δ = b2-4ac
Δ = 4602-4·27·48
Δ = 206416
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:

$\sqrt{\Delta}=\sqrt{206416}=\sqrt{16*12901}=\sqrt{16}*\sqrt{12901}=4\sqrt{12901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(460)-4\sqrt{12901}}{2*27}=\frac{-460-4\sqrt{12901}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(460)+4\sqrt{12901}}{2*27}=\frac{-460+4\sqrt{12901}}{54}
$