3x^2+11x+7=x

Solution for 3x^2+11x+7=x equation:

3x^2+11x+7=x

We move all terms to the left:

3x^2+11x+7-(x)=0

We add all the numbers together, and all the variables

3x^2+10x+7=0

a = 3; b = 10; c = +7;
Δ = b2-4ac
Δ = 102-4·3·7
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*3}=\frac{-6}{6}
=-1
$