3x(2x-1)=-8x+4

Solution for 3x(2x-1)=-8x+4 equation:

3x(2x-1)=-8x+4

We move all terms to the left:

3x(2x-1)-(-8x+4)=0

We multiply parentheses

6x^2-3x-(-8x+4)=0

We get rid of parentheses

6x^2-3x+8x-4=0

We add all the numbers together, and all the variables

6x^2+5x-4=0

a = 6; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·6·(-4)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*6}=\frac{-16}{12}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*6}=\frac{6}{12}
=1/2
$