7/8x-1=1/4x+4

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

7/8x-1=1/4x+4

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



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

x∈R


We get rid of parentheses

7/8x-1/4x-4-1=0

We calculate fractions


28x/32x^2+(-8x)/32x^2-4-1=0

We add all the numbers together, and all the variables

28x/32x^2+(-8x)/32x^2-5=0

We multiply all the terms by the denominator


28x+(-8x)-5*32x^2=0

Wy multiply elements

-160x^2+28x+(-8x)=0

We get rid of parentheses

-160x^2+28x-8x=0

We add all the numbers together, and all the variables

-160x^2+20x=0

a = -160; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-160)·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*-160}=\frac{-40}{-320}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-160}=\frac{0}{-320}
=0
$