4/5x+3=2x-1

Solution for 4/5x+3=2x-1 equation:

4/5x+3=2x-1

We move all terms to the left:

4/5x+3-(2x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-2x+1+3=0

We multiply all the terms by the denominator


-2x*5x+1*5x+3*5x+4=0

Wy multiply elements

-10x^2+5x+15x+4=0

We add all the numbers together, and all the variables

-10x^2+20x+4=0

a = -10; b = 20; c = +4;
Δ = b2-4ac
Δ = 202-4·(-10)·4
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{35}}{2*-10}=\frac{-20-4\sqrt{35}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{35}}{2*-10}=\frac{-20+4\sqrt{35}}{-20}
$