4=3x^2+5x+2

Solution for 4=3x^2+5x+2 equation:

4=3x^2+5x+2

We move all terms to the left:

4-(3x^2+5x+2)=0

We get rid of parentheses

-3x^2-5x-2+4=0

We add all the numbers together, and all the variables

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

a = -3; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-3)·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*-3}=\frac{-2}{-6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-3}=\frac{12}{-6}
=-2
$