7/8x=4/5x+2

Solution for 7/8x=4/5x+2 equation:

7/8x=4/5x+2

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


35x/40x^2+(-32x)/40x^2-2=0

We multiply all the terms by the denominator


35x+(-32x)-2*40x^2=0

Wy multiply elements

-80x^2+35x+(-32x)=0

We get rid of parentheses

-80x^2+35x-32x=0

We add all the numbers together, and all the variables

-80x^2+3x=0

a = -80; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-80)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-80}=\frac{-6}{-160}
=3/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-80}=\frac{0}{-160}
=0
$