8x^2+48x+27=0

Solution for 8x^2+48x+27=0 equation:

8x^2+48x+27=0

a = 8; b = 48; c = +27;
Δ = b2-4ac
Δ = 482-4·8·27
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{10}}{2*8}=\frac{-48-12\sqrt{10}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{10}}{2*8}=\frac{-48+12\sqrt{10}}{16}
$