4/5x-x=-19

Solution for 4/5x-x=-19 equation:

4/5x-x=-19

We move all terms to the left:

4/5x-x-(-19)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/5x+19=0

We multiply all the terms by the denominator


-1x*5x+19*5x+4=0

Wy multiply elements

-5x^2+95x+4=0

a = -5; b = 95; c = +4;
Δ = b2-4ac
Δ = 952-4·(-5)·4
Δ = 9105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(95)-\sqrt{9105}}{2*-5}=\frac{-95-\sqrt{9105}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(95)+\sqrt{9105}}{2*-5}=\frac{-95+\sqrt{9105}}{-10}
$