4x2-x=8x-2x2

Solution for 4x2-x=8x-2x2 equation:

4x^2-x=8x-2x^2

We move all terms to the left:

4x^2-x-(8x-2x^2)=0

We add all the numbers together, and all the variables

4x^2-(8x-2x^2)-1x=0

We get rid of parentheses

4x^2+2x^2-8x-1x=0

We add all the numbers together, and all the variables

6x^2-9x=0

a = 6; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·6·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*6}=\frac{18}{12}
=1+1/2
$