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

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

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

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-3000x^2)/4000x^2+3500x/4000x^2+(-384x)/4000x^2+512x/4000x^2=0

We multiply all the terms by the denominator


(-3000x^2)+3500x+(-384x)+512x=0

We add all the numbers together, and all the variables

(-3000x^2)+4012x+(-384x)=0

We get rid of parentheses

-3000x^2+4012x-384x=0

We add all the numbers together, and all the variables

-3000x^2+3628x=0

a = -3000; b = 3628; c = 0;
Δ = b2-4ac
Δ = 36282-4·(-3000)·0
Δ = 13162384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13162384}=3628$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3628)-3628}{2*-3000}=\frac{-7256}{-6000}
=1+157/750
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3628)+3628}{2*-3000}=\frac{0}{-6000}
=0
$