7/8x-1/2=3/10x+5

Solution for 7/8x-1/2=3/10x+5 equation:

7/8x-1/2=3/10x+5

We move all terms to the left:

7/8x-1/2-(3/10x+5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 10x+5)!=0

x∈R


We get rid of parentheses

7/8x-3/10x-5-1/2=0

We calculate fractions


(-80x^2)/320x^2+280x/320x^2+(-96x)/320x^2-5=0

We multiply all the terms by the denominator


(-80x^2)+280x+(-96x)-5*320x^2=0

Wy multiply elements

(-80x^2)-1600x^2+280x+(-96x)=0

We get rid of parentheses

-80x^2-1600x^2+280x-96x=0

We add all the numbers together, and all the variables

-1680x^2+184x=0

a = -1680; b = 184; c = 0;
Δ = b2-4ac
Δ = 1842-4·(-1680)·0
Δ = 33856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33856}=184$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(184)-184}{2*-1680}=\frac{-368}{-3360}
=23/210
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(184)+184}{2*-1680}=\frac{0}{-3360}
=0
$