x(4x.x-3)=1/5

Solution for x(4x.x-3)=1/5 equation:

x(4x.x-3)=1/5

We move all terms to the left:

x(4x.x-3)-(1/5)=0

We add all the numbers together, and all the variables

x(4x.x-3)-(+1/5)=0

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

20x^2-15x-1=0

a = 20; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·20·(-1)
Δ = 305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{305}}{2*20}=\frac{15-\sqrt{305}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{305}}{2*20}=\frac{15+\sqrt{305}}{40}
$