2/5x+1=4x+3

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

2/5x+1=4x+3

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-20x^2-15x+5x+2=0

We add all the numbers together, and all the variables

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

a = -20; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·(-20)·2
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{65}}{2*-20}=\frac{10-2\sqrt{65}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{65}}{2*-20}=\frac{10+2\sqrt{65}}{-40}
$