6x2+9=-55x

Solution for 6x2+9=-55x equation:

6x^2+9=-55x

We move all terms to the left:

6x^2+9-(-55x)=0

We get rid of parentheses

6x^2+55x+9=0

a = 6; b = 55; c = +9;
Δ = b2-4ac
Δ = 552-4·6·9
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-53}{2*6}=\frac{-108}{12}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+53}{2*6}=\frac{-2}{12}
=-1/6
$