-3x^2-8x+7=-2

Solution for -3x^2-8x+7=-2 equation:

-3x^2-8x+7=-2

We move all terms to the left:

-3x^2-8x+7-(-2)=0

We add all the numbers together, and all the variables

-3x^2-8x+9=0

a = -3; b = -8; c = +9;
Δ = b2-4ac
Δ = -82-4·(-3)·9
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{43}}{2*-3}=\frac{8-2\sqrt{43}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{43}}{2*-3}=\frac{8+2\sqrt{43}}{-6}
$