-11x=6+5x^2

Solution for -11x=6+5x^2 equation:

-11x=6+5x^2

We move all terms to the left:

-11x-(6+5x^2)=0

We get rid of parentheses

-5x^2-11x-6=0

a = -5; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·(-5)·(-6)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*-5}=\frac{10}{-10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*-5}=\frac{12}{-10}
=-1+1/5
$