(4x^2)/3=4x-2

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

(4x^2)/3=4x-2

We move all terms to the left:

(4x^2)/3-(4x-2)=0

We get rid of parentheses

4x^2/3-4x+2=0

We multiply all the terms by the denominator


4x^2-4x*3+2*3=0

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-12x+6=0

a = 4; b = -12; c = +6;
Δ = b2-4ac
Δ = -122-4·4·6
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*4}=\frac{12-4\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*4}=\frac{12+4\sqrt{3}}{8}
$