2x^2+1-17x=-2x^2+6+2x

Solution for 2x^2+1-17x=-2x^2+6+2x equation:

2x^2+1-17x=-2x^2+6+2x

We move all terms to the left:

2x^2+1-17x-(-2x^2+6+2x)=0

We get rid of parentheses

2x^2+2x^2-2x-17x-6+1=0

We add all the numbers together, and all the variables

4x^2-19x-5=0

a = 4; b = -19; c = -5;
Δ = b2-4ac
Δ = -192-4·4·(-5)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-21}{2*4}=\frac{-2}{8}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+21}{2*4}=\frac{40}{8}
=5
$