X+30/8=1x/4x

Solution for X+30/8=1x/4x equation:

X+30/8=1X/4X

We move all terms to the left:

X+30/8-(1X/4X)=0


Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1X/4X)+30/8=0

We get rid of parentheses

X-1X/4X+30/8=0

We calculate fractions


X+(-8X)/32X+120X/32X=0

We multiply all the terms by the denominator


X*32X+(-8X)+120X=0

We add all the numbers together, and all the variables

120X+X*32X+(-8X)=0

Wy multiply elements

32X^2+120X+(-8X)=0

We get rid of parentheses

32X^2+120X-8X=0

We add all the numbers together, and all the variables

32X^2+112X=0

a = 32; b = 112; c = 0;
Δ = b2-4ac
Δ = 1122-4·32·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-112}{2*32}=\frac{-224}{64}
=-3+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*32}=\frac{0}{64}
=0
$