9(x)=3x^2-5+1

Solution for 9(x)=3x^2-5+1 equation:

9(x)=3x^2-5+1

We move all terms to the left:

9(x)-(3x^2-5+1)=0

We get rid of parentheses

-3x^2+9x+5-1=0

We add all the numbers together, and all the variables

-3x^2+9x+4=0

a = -3; b = 9; c = +4;
Δ = b2-4ac
Δ = 92-4·(-3)·4
Δ = 129
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{-(9)-\sqrt{129}}{2*-3}=\frac{-9-\sqrt{129}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*-3}=\frac{-9+\sqrt{129}}{-6}
$