21/2x-3/42x+5=3/8

Solution for 21/2x-3/42x+5=3/8 equation:

21/2x-3/42x+5=3/8

We move all terms to the left:

21/2x-3/42x+5-(3/8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 42x!=0

x!=0/42

x!=0

x∈R


We add all the numbers together, and all the variables

21/2x-3/42x+5-(+3/8)=0

We get rid of parentheses

21/2x-3/42x+5-3/8=0

We calculate fractions


(-1008x^2)/5376x^2+56448x/5376x^2+(-384x)/5376x^2+5=0

We multiply all the terms by the denominator


(-1008x^2)+56448x+(-384x)+5*5376x^2=0

Wy multiply elements

(-1008x^2)+26880x^2+56448x+(-384x)=0

We get rid of parentheses

-1008x^2+26880x^2+56448x-384x=0

We add all the numbers together, and all the variables

25872x^2+56064x=0

a = 25872; b = 56064; c = 0;
Δ = b2-4ac
Δ = 560642-4·25872·0
Δ = 3143172096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3143172096}=56064$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56064)-56064}{2*25872}=\frac{-112128}{51744}
=-2+90/539
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56064)+56064}{2*25872}=\frac{0}{51744}
=0
$