4/5x+3=4x-8

Solution for 4/5x+3=4x-8 equation:

4/5x+3=4x-8

We move all terms to the left:

4/5x+3-(4x-8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-4x+8+3=0

We multiply all the terms by the denominator


-4x*5x+8*5x+3*5x+4=0

Wy multiply elements

-20x^2+40x+15x+4=0

We add all the numbers together, and all the variables

-20x^2+55x+4=0

a = -20; b = 55; c = +4;
Δ = b2-4ac
Δ = 552-4·(-20)·4
Δ = 3345
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{-(55)-\sqrt{3345}}{2*-20}=\frac{-55-\sqrt{3345}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3345}}{2*-20}=\frac{-55+\sqrt{3345}}{-40}
$