5/4x-7/8x=30

Solution for 5/4x-7/8x=30 equation:

5/4x-7/8x=30

We move all terms to the left:

5/4x-7/8x-(30)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


40x/32x^2+(-28x)/32x^2-30=0

We multiply all the terms by the denominator


40x+(-28x)-30*32x^2=0

Wy multiply elements

-960x^2+40x+(-28x)=0

We get rid of parentheses

-960x^2+40x-28x=0

We add all the numbers together, and all the variables

-960x^2+12x=0

a = -960; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-960)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-960}=\frac{-24}{-1920}
=1/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-960}=\frac{0}{-1920}
=0
$