6x(-x-10)=55+x

Solution for 6x(-x-10)=55+x equation:

6x(-x-10)=55+x

We move all terms to the left:

6x(-x-10)-(55+x)=0

We add all the numbers together, and all the variables

6x(-1x-10)-(x+55)=0

We multiply parentheses

-6x^2-60x-(x+55)=0

We get rid of parentheses

-6x^2-60x-x-55=0

We add all the numbers together, and all the variables

-6x^2-61x-55=0

a = -6; b = -61; c = -55;
Δ = b2-4ac
Δ = -612-4·(-6)·(-55)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-49}{2*-6}=\frac{12}{-12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+49}{2*-6}=\frac{110}{-12}
=-9+1/6
$