4/5x+16=x-20

Solution for 4/5x+16=x-20 equation:

4/5x+16=x-20

We move all terms to the left:

4/5x+16-(x-20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-x+20+16=0

We multiply all the terms by the denominator


-x*5x+20*5x+16*5x+4=0

Wy multiply elements

-5x^2+100x+80x+4=0

We add all the numbers together, and all the variables

-5x^2+180x+4=0

a = -5; b = 180; c = +4;
Δ = b2-4ac
Δ = 1802-4·(-5)·4
Δ = 32480
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:

$\sqrt{\Delta}=\sqrt{32480}=\sqrt{16*2030}=\sqrt{16}*\sqrt{2030}=4\sqrt{2030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{2030}}{2*-5}=\frac{-180-4\sqrt{2030}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{2030}}{2*-5}=\frac{-180+4\sqrt{2030}}{-10}
$