9/5x-1/8=3/4x

Solution for 9/5x-1/8=3/4x equation:

9/5x-1/8=3/4x

We move all terms to the left:

9/5x-1/8-(3/4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/5x-(+3/4x)-1/8=0

We get rid of parentheses

9/5x-3/4x-1/8=0

We calculate fractions


(-80x^2)/1280x^2+2304x/1280x^2+(-960x)/1280x^2=0

We multiply all the terms by the denominator


(-80x^2)+2304x+(-960x)=0

We get rid of parentheses

-80x^2+2304x-960x=0

We add all the numbers together, and all the variables

-80x^2+1344x=0

a = -80; b = 1344; c = 0;
Δ = b2-4ac
Δ = 13442-4·(-80)·0
Δ = 1806336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1806336}=1344$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1344)-1344}{2*-80}=\frac{-2688}{-160}
=16+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1344)+1344}{2*-80}=\frac{0}{-160}
=0
$