3/4x+7=27+1/8x

Solution for 3/4x+7=27+1/8x equation:

3/4x+7=27+1/8x

We move all terms to the left:

3/4x+7-(27+1/8x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(1/8x+27)+7=0

We get rid of parentheses

3/4x-1/8x-27+7=0

We calculate fractions


24x/32x^2+(-4x)/32x^2-27+7=0

We add all the numbers together, and all the variables

24x/32x^2+(-4x)/32x^2-20=0

We multiply all the terms by the denominator


24x+(-4x)-20*32x^2=0

Wy multiply elements

-640x^2+24x+(-4x)=0

We get rid of parentheses

-640x^2+24x-4x=0

We add all the numbers together, and all the variables

-640x^2+20x=0

a = -640; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-640)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-640}=\frac{-40}{-1280}
=1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-640}=\frac{0}{-1280}
=0
$