3x+1/2=-6x(x+4)/4

Solution for 3x+1/2=-6x(x+4)/4 equation:

3x+1/2=-6x(x+4)/4

We move all terms to the left:

3x+1/2-(-6x(x+4)/4)=0

We calculate fractions


3x+(-(-6x(x+4)*2)/()+()/()=0


We calculate terms in parentheses: +(-(-6x(x+4)*2)/()+()/(), so:

-(-6x(x+4)*2)/()+()/(

We add all the numbers together, and all the variables

-(-6x(x+4)*2)/()+1

We multiply all the terms by the denominator


-(-6x(x+4)*2)+1*()


We calculate terms in parentheses: -(-6x(x+4)*2), so:

-6x(x+4)*2

We multiply parentheses

-12x^2-48x

Back to the equation:

-(-12x^2-48x)


We add all the numbers together, and all the variables

-(-12x^2-48x)

We get rid of parentheses

12x^2+48x

Back to the equation:

+(12x^2+48x)


We get rid of parentheses

12x^2+3x+48x=0

We add all the numbers together, and all the variables

12x^2+51x=0

a = 12; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·12·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*12}=\frac{-102}{24}
=-4+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*12}=\frac{0}{24}
=0
$