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

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

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

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


10x/16x^2+(-8x)/16x^2-2-10=0

We add all the numbers together, and all the variables

10x/16x^2+(-8x)/16x^2-12=0

We multiply all the terms by the denominator


10x+(-8x)-12*16x^2=0

Wy multiply elements

-192x^2+10x+(-8x)=0

We get rid of parentheses

-192x^2+10x-8x=0

We add all the numbers together, and all the variables

-192x^2+2x=0

a = -192; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-192)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-192}=\frac{-4}{-384}
=1/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-192}=\frac{0}{-384}
=0
$