8/5x+1-7/8x=3/4

Solution for 8/5x+1-7/8x=3/4 equation:

8/5x+1-7/8x=3/4

We move all terms to the left:

8/5x+1-7/8x-(3/4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

8/5x-7/8x+1-(+3/4)=0

We get rid of parentheses

8/5x-7/8x+1-3/4=0

We calculate fractions


(-960x^2)/640x^2+1024x/640x^2+(-560x)/640x^2+1=0

We multiply all the terms by the denominator


(-960x^2)+1024x+(-560x)+1*640x^2=0

Wy multiply elements

(-960x^2)+640x^2+1024x+(-560x)=0

We get rid of parentheses

-960x^2+640x^2+1024x-560x=0

We add all the numbers together, and all the variables

-320x^2+464x=0

a = -320; b = 464; c = 0;
Δ = b2-4ac
Δ = 4642-4·(-320)·0
Δ = 215296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{215296}=464$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(464)-464}{2*-320}=\frac{-928}{-640}
=1+9/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(464)+464}{2*-320}=\frac{0}{-640}
=0
$