11=x(6x+5)

Solution for 11=x(6x+5) equation:

11=x(6x+5)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(6x+5)), so:

x(6x+5)

We multiply parentheses

6x^2+5x

Back to the equation:

-(6x^2+5x)


We get rid of parentheses

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

a = -6; b = -5; c = +11;
Δ = b2-4ac
Δ = -52-4·(-6)·11
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-17}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+17}{2*-6}=\frac{22}{-12}
=-1+5/6
$