3x2+4x=1/27

Solution for 3x2+4x=1/27 equation:

3x^2+4x=1/27

We move all terms to the left:

3x^2+4x-(1/27)=0

We add all the numbers together, and all the variables

3x^2+4x-(+1/27)=0

We get rid of parentheses

3x^2+4x-1/27=0

We multiply all the terms by the denominator


3x^2*27+4x*27-1=0

Wy multiply elements

81x^2+108x-1=0

a = 81; b = 108; c = -1;
Δ = b2-4ac
Δ = 1082-4·81·(-1)
Δ = 11988
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:

$\sqrt{\Delta}=\sqrt{11988}=\sqrt{324*37}=\sqrt{324}*\sqrt{37}=18\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-18\sqrt{37}}{2*81}=\frac{-108-18\sqrt{37}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+18\sqrt{37}}{2*81}=\frac{-108+18\sqrt{37}}{162}
$