12=11x+5x^2

Solution for 12=11x+5x^2 equation:

12=11x+5x^2

We move all terms to the left:

12-(11x+5x^2)=0

We get rid of parentheses

-5x^2-11x+12=0

a = -5; b = -11; c = +12;
Δ = b2-4ac
Δ = -112-4·(-5)·12
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-19}{2*-5}=\frac{-8}{-10}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+19}{2*-5}=\frac{30}{-10}
=-3
$