3x^2-4=8X-1/5

Solution for 3x^2-4=8X-1/5 equation:

3x^2-4=8x-1/5

We move all terms to the left:

3x^2-4-(8x-1/5)=0

We add all the numbers together, and all the variables

3x^2-(+8x-1/5)-4=0

We get rid of parentheses

3x^2-8x-4+1/5=0

We multiply all the terms by the denominator


3x^2*5-8x*5+1-4*5=0

We add all the numbers together, and all the variables

3x^2*5-8x*5-19=0

Wy multiply elements

15x^2-40x-19=0

a = 15; b = -40; c = -19;
Δ = b2-4ac
Δ = -402-4·15·(-19)
Δ = 2740
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:

$\sqrt{\Delta}=\sqrt{2740}=\sqrt{4*685}=\sqrt{4}*\sqrt{685}=2\sqrt{685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{685}}{2*15}=\frac{40-2\sqrt{685}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{685}}{2*15}=\frac{40+2\sqrt{685}}{30}
$