4x^2-2x=127/3

Solution for 4x^2-2x=127/3 equation:

4x^2-2x=127/3

We move all terms to the left:

4x^2-2x-(127/3)=0

We add all the numbers together, and all the variables

4x^2-2x-(+127/3)=0

We get rid of parentheses

4x^2-2x-127/3=0

We multiply all the terms by the denominator


4x^2*3-2x*3-127=0

Wy multiply elements

12x^2-6x-127=0

a = 12; b = -6; c = -127;
Δ = b2-4ac
Δ = -62-4·12·(-127)
Δ = 6132
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:

$\sqrt{\Delta}=\sqrt{6132}=\sqrt{4*1533}=\sqrt{4}*\sqrt{1533}=2\sqrt{1533}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{1533}}{2*12}=\frac{6-2\sqrt{1533}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{1533}}{2*12}=\frac{6+2\sqrt{1533}}{24}
$