2x^2-x=52/6

Solution for 2x^2-x=52/6 equation:

2x^2-x=52/6

We move all terms to the left:

2x^2-x-(52/6)=0

We add all the numbers together, and all the variables

2x^2-x-(+52/6)=0

We add all the numbers together, and all the variables

2x^2-1x-(+52/6)=0

We get rid of parentheses

2x^2-1x-52/6=0

We multiply all the terms by the denominator


2x^2*6-1x*6-52=0

Wy multiply elements

12x^2-6x-52=0

a = 12; b = -6; c = -52;
Δ = b2-4ac
Δ = -62-4·12·(-52)
Δ = 2532
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:

$\sqrt{\Delta}=\sqrt{2532}=\sqrt{4*633}=\sqrt{4}*\sqrt{633}=2\sqrt{633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{633}}{2*12}=\frac{6-2\sqrt{633}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{633}}{2*12}=\frac{6+2\sqrt{633}}{24}
$