5x^2-2x=122/3

Solution for 5x^2-2x=122/3 equation:

5x^2-2x=122/3

We move all terms to the left:

5x^2-2x-(122/3)=0

We add all the numbers together, and all the variables

5x^2-2x-(+122/3)=0

We get rid of parentheses

5x^2-2x-122/3=0

We multiply all the terms by the denominator


5x^2*3-2x*3-122=0

Wy multiply elements

15x^2-6x-122=0

a = 15; b = -6; c = -122;
Δ = b2-4ac
Δ = -62-4·15·(-122)
Δ = 7356
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:

$\sqrt{\Delta}=\sqrt{7356}=\sqrt{4*1839}=\sqrt{4}*\sqrt{1839}=2\sqrt{1839}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{1839}}{2*15}=\frac{6-2\sqrt{1839}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{1839}}{2*15}=\frac{6+2\sqrt{1839}}{30}
$