3(x+3)+5=3x2

Solution for 3(x+3)+5=3x2 equation:

3(x+3)+5=3x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-3x^2+3(x+3)+5=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-3x^2+3x+14=0

a = -3; b = 3; c = +14;
Δ = b2-4ac
Δ = 32-4·(-3)·14
Δ = 177
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{-(3)-\sqrt{177}}{2*-3}=\frac{-3-\sqrt{177}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{177}}{2*-3}=\frac{-3+\sqrt{177}}{-6}
$