(-5.5)=4x^2+24x+11

Solution for (-5.5)=4x^2+24x+11 equation:

(-5.5)=4x^2+24x+11

We move all terms to the left:

(-5.5)-(4x^2+24x+11)=0

We add all the numbers together, and all the variables

-(4x^2+24x+11)-5.5=0

We get rid of parentheses

-4x^2-24x-11-5.5=0

We add all the numbers together, and all the variables

-4x^2-24x-16.5=0

a = -4; b = -24; c = -16.5;
Δ = b2-4ac
Δ = -242-4·(-4)·(-16.5)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{78}}{2*-4}=\frac{24-2\sqrt{78}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{78}}{2*-4}=\frac{24+2\sqrt{78}}{-8}
$