4/5x+19=x-1

Solution for 4/5x+19=x-1 equation:

4/5x+19=x-1

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-5x^2+100x+4=0

a = -5; b = 100; c = +4;
Δ = b2-4ac
Δ = 1002-4·(-5)·4
Δ = 10080
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10080}=\sqrt{144*70}=\sqrt{144}*\sqrt{70}=12\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-12\sqrt{70}}{2*-5}=\frac{-100-12\sqrt{70}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+12\sqrt{70}}{2*-5}=\frac{-100+12\sqrt{70}}{-10}
$