3x2+4(x+1/4)=0

Solution for 3x2+4(x+1/4)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2+4x+1/4*4=0

We multiply all the terms by the denominator


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

Wy multiply elements

48x^2*4+64x*4+1=0

Wy multiply elements

192x^2+256x+1=0

a = 192; b = 256; c = +1;
Δ = b2-4ac
Δ = 2562-4·192·1
Δ = 64768
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:

$\sqrt{\Delta}=\sqrt{64768}=\sqrt{256*253}=\sqrt{256}*\sqrt{253}=16\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(256)-16\sqrt{253}}{2*192}=\frac{-256-16\sqrt{253}}{384}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(256)+16\sqrt{253}}{2*192}=\frac{-256+16\sqrt{253}}{384}
$