10x-4=4x(3-2x)

Solution for 10x-4=4x(3-2x) equation:

10x-4=4x(3-2x)

We move all terms to the left:

10x-4-(4x(3-2x))=0

We add all the numbers together, and all the variables

10x-(4x(-2x+3))-4=0


We calculate terms in parentheses: -(4x(-2x+3)), so:

4x(-2x+3)

We multiply parentheses

-8x^2+12x

Back to the equation:

-(-8x^2+12x)


We get rid of parentheses

8x^2-12x+10x-4=0

We add all the numbers together, and all the variables

8x^2-2x-4=0

a = 8; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·8·(-4)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{33}}{2*8}=\frac{2-2\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{33}}{2*8}=\frac{2+2\sqrt{33}}{16}
$