23-3x2=5+3x

Solution for 23-3x2=5+3x equation:

23-3x^2=5+3x

We move all terms to the left:

23-3x^2-(5+3x)=0

We add all the numbers together, and all the variables

-3x^2-(3x+5)+23=0

We get rid of parentheses

-3x^2-3x-5+23=0

We add all the numbers together, and all the variables

-3x^2-3x+18=0

a = -3; b = -3; c = +18;
Δ = b2-4ac
Δ = -32-4·(-3)·18
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*-3}=\frac{18}{-6}
=-3
$