19-5/2x=34+5/8x

Solution for 19-5/2x=34+5/8x equation:

19-5/2x=34+5/8x

We move all terms to the left:

19-5/2x-(34+5/8x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-5/2x-(5/8x+34)+19=0

We get rid of parentheses

-5/2x-5/8x-34+19=0

We calculate fractions


(-40x)/16x^2+(-10x)/16x^2-34+19=0

We add all the numbers together, and all the variables

(-40x)/16x^2+(-10x)/16x^2-15=0

We multiply all the terms by the denominator


(-40x)+(-10x)-15*16x^2=0

Wy multiply elements

-240x^2+(-40x)+(-10x)=0

We get rid of parentheses

-240x^2-40x-10x=0

We add all the numbers together, and all the variables

-240x^2-50x=0

a = -240; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·(-240)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*-240}=\frac{0}{-480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*-240}=\frac{100}{-480}
=-5/24
$