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

Solution for X^2+5x+2=3x^2-x-2 equation:

X^2+5X+2=3X^2-X-2

We move all terms to the left:

X^2+5X+2-(3X^2-X-2)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2X^2+6X+4=0

a = -2; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-2)·4
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*-2}=\frac{-6-2\sqrt{17}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*-2}=\frac{-6+2\sqrt{17}}{-4}
$