2*x^2+3*x+3*x^2=3

Solution for 2*x^2+3*x+3*x^2=3 equation:

2x^2+3x+3x^2=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

5x^2+3x-3=0

a = 5; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·5·(-3)
Δ = 69
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{69}}{2*5}=\frac{-3-\sqrt{69}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{69}}{2*5}=\frac{-3+\sqrt{69}}{10}
$