3/4x+5/12x-2/3=-3

Solution for 3/4x+5/12x-2/3=-3 equation:

3/4x+5/12x-2/3=-3

We move all terms to the left:

3/4x+5/12x-2/3-(-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x+5/12x+3-2/3=0

We calculate fractions


(-96x^2)/432x^2+324x/432x^2+180x/432x^2+3=0

We multiply all the terms by the denominator


(-96x^2)+324x+180x+3*432x^2=0

We add all the numbers together, and all the variables

(-96x^2)+504x+3*432x^2=0

Wy multiply elements

(-96x^2)+1296x^2+504x=0

We get rid of parentheses

-96x^2+1296x^2+504x=0

We add all the numbers together, and all the variables

1200x^2+504x=0

a = 1200; b = 504; c = 0;
Δ = b2-4ac
Δ = 5042-4·1200·0
Δ = 254016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{254016}=504$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(504)-504}{2*1200}=\frac{-1008}{2400}
=-21/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(504)+504}{2*1200}=\frac{0}{2400}
=0
$