4/5x+8=19+15x

Solution for 4/5x+8=19+15x equation:

4/5x+8=19+15x

We move all terms to the left:

4/5x+8-(19+15x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(15x+19)+8=0

We get rid of parentheses

4/5x-15x-19+8=0

We multiply all the terms by the denominator


-15x*5x-19*5x+8*5x+4=0

Wy multiply elements

-75x^2-95x+40x+4=0

We add all the numbers together, and all the variables

-75x^2-55x+4=0

a = -75; b = -55; c = +4;
Δ = b2-4ac
Δ = -552-4·(-75)·4
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-65}{2*-75}=\frac{-10}{-150}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+65}{2*-75}=\frac{120}{-150}
=-4/5
$