3x2-x=11

Solution for 3x2-x=11 equation:

3x^2-x=11

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-1x-11=0

a = 3; b = -1; c = -11;
Δ = b2-4ac
Δ = -12-4·3·(-11)
Δ = 133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{133}}{2*3}=\frac{1-\sqrt{133}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{133}}{2*3}=\frac{1+\sqrt{133}}{6}
$