7-3x^2=2x+1

Solution for 7-3x^2=2x+1 equation:

7-3x^2=2x+1

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2-2x+6=0

a = -3; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-3)·6
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*-3}=\frac{2-2\sqrt{19}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*-3}=\frac{2+2\sqrt{19}}{-6}
$