24x^2=-114x-27

Solution for 24x^2=-114x-27 equation:

24x^2=-114x-27

We move all terms to the left:

24x^2-(-114x-27)=0

We get rid of parentheses

24x^2+114x+27=0

a = 24; b = 114; c = +27;
Δ = b2-4ac
Δ = 1142-4·24·27
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-102}{2*24}=\frac{-216}{48}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+102}{2*24}=\frac{-12}{48}
=-1/4
$