3x+2x^2+4=4x^2+3

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

3x+2x^2+4=4x^2+3

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-2)·1
Δ = 17
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{17}}{2*-2}=\frac{-3-\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{17}}{2*-2}=\frac{-3+\sqrt{17}}{-4}
$