11x+3x^2=14

Solution for 11x+3x^2=14 equation:

11x+3x^2=14

We move all terms to the left:

11x+3x^2-(14)=0

a = 3; b = 11; c = -14;
Δ = b2-4ac
Δ = 112-4·3·(-14)
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{-(11)-17}{2*3}=\frac{-28}{6}
=-4+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+17}{2*3}=\frac{6}{6}
=1
$