(7)=3x^2+2x-9=0

Solution for (7)=3x^2+2x-9=0 equation:

(7)=3x^2+2x-9=0

We move all terms to the left:

(7)-(3x^2+2x-9)=0

We get rid of parentheses

-3x^2-2x+9+7=0

We add all the numbers together, and all the variables

-3x^2-2x+16=0

a = -3; b = -2; c = +16;
Δ = b2-4ac
Δ = -22-4·(-3)·16
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*-3}=\frac{16}{-6}
=-2+2/3
$