6x/3+x=-4x^2

Solution for 6x/3+x=-4x^2 equation:

6x/3+x=-4x^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

4x^2+x+6x/3=0

We multiply all the terms by the denominator


4x^2*3+x*3+6x=0

We add all the numbers together, and all the variables

4x^2*3+6x+x*3=0

Wy multiply elements

12x^2+6x+3x=0

We add all the numbers together, and all the variables

12x^2+9x=0

a = 12; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·12·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*12}=\frac{-18}{24}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*12}=\frac{0}{24}
=0
$