3x2/4(x+2)=-3/8

Solution for 3x2/4(x+2)=-3/8 equation:

3x^2/4(x+2)=-3/8

We move all terms to the left:

3x^2/4(x+2)-(-3/8)=0


Domain of the equation: 4(x+2)!=0

x∈R


We get rid of parentheses

3x^2/4(x+2)+3/8=0

We calculate fractions


24x^2/(32x+64)+(12xx/(32x+64)=0


We calculate terms in parentheses: +(12xx/(32x+64), so:

12xx/(32x+64

We multiply all the terms by the denominator


12xx

Back to the equation:

+(12xx)


We multiply all the terms by the denominator


24x^2+12xx*(32x+64)=0

We multiply parentheses

24x^2+384x^2+768x=0

We add all the numbers together, and all the variables

408x^2+768x=0

a = 408; b = 768; c = 0;
Δ = b2-4ac
Δ = 7682-4·408·0
Δ = 589824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{589824}=768$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(768)-768}{2*408}=\frac{-1536}{816}
=-1+15/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(768)+768}{2*408}=\frac{0}{816}
=0
$