-3x2+7=x

Solution for -3x2+7=x equation:

-3x^2+7=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-3x^2-1x+7=0

a = -3; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-3)·7
Δ = 85
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{85}}{2*-3}=\frac{1-\sqrt{85}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{85}}{2*-3}=\frac{1+\sqrt{85}}{-6}
$