X^2+1+4x=2x^2+3x-2

Solution for X^2+1+4x=2x^2+3x-2 equation:

X^2+1+4X=2X^2+3X-2

We move all terms to the left:

X^2+1+4X-(2X^2+3X-2)=0

We get rid of parentheses

X^2-2X^2+4X-3X+2+1=0

We add all the numbers together, and all the variables

-1X^2+X+3=0

a = -1; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-1)·3
Δ = 13
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{-(1)-\sqrt{13}}{2*-1}=\frac{-1-\sqrt{13}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*-1}=\frac{-1+\sqrt{13}}{-2}
$