24x^2=-112x-27

Solution for 24x^2=-112x-27 equation:

24x^2=-112x-27

We move all terms to the left:

24x^2-(-112x-27)=0

We get rid of parentheses

24x^2+112x+27=0

a = 24; b = 112; c = +27;
Δ = b2-4ac
Δ = 1122-4·24·27
Δ = 9952
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:

$\sqrt{\Delta}=\sqrt{9952}=\sqrt{16*622}=\sqrt{16}*\sqrt{622}=4\sqrt{622}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{622}}{2*24}=\frac{-112-4\sqrt{622}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{622}}{2*24}=\frac{-112+4\sqrt{622}}{48}
$