3x2+14x=-11

Solution for 3x2+14x=-11 equation:

3x^2+14x=-11

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2+14x+11=0

a = 3; b = 14; c = +11;
Δ = b2-4ac
Δ = 142-4·3·11
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8}{2*3}=\frac{-22}{6}
=-3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8}{2*3}=\frac{-6}{6}
=-1
$