2x+3x^2=11

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

2x+3x^2=11

We move all terms to the left:

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

a = 3; b = 2; c = -11;
Δ = b2-4ac
Δ = 22-4·3·(-11)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{34}}{2*3}=\frac{-2-2\sqrt{34}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{34}}{2*3}=\frac{-2+2\sqrt{34}}{6}
$