2/5*x-7/8=3/4*x

Solution for 2/5*x-7/8=3/4*x equation:

2/5x-7/8=3/4x

We move all terms to the left:

2/5x-7/8-(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

2/5x-(+3/4x)-7/8=0

We get rid of parentheses

2/5x-3/4x-7/8=0

We calculate fractions


(-560x^2)/1280x^2+512x/1280x^2+(-960x)/1280x^2=0

We multiply all the terms by the denominator


(-560x^2)+512x+(-960x)=0

We get rid of parentheses

-560x^2+512x-960x=0

We add all the numbers together, and all the variables

-560x^2-448x=0

a = -560; b = -448; c = 0;
Δ = b2-4ac
Δ = -4482-4·(-560)·0
Δ = 200704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{200704}=448$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-448)-448}{2*-560}=\frac{0}{-1120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-448)+448}{2*-560}=\frac{896}{-1120}
=-4/5
$