3/5x+2x+18=4x-1

Solution for 3/5x+2x+18=4x-1 equation:

3/5x+2x+18=4x-1

We move all terms to the left:

3/5x+2x+18-(4x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/5x-(4x-1)+18=0

We get rid of parentheses

2x+3/5x-4x+1+18=0

We multiply all the terms by the denominator


2x*5x-4x*5x+1*5x+18*5x+3=0

Wy multiply elements

10x^2-20x^2+5x+90x+3=0

We add all the numbers together, and all the variables

-10x^2+95x+3=0

a = -10; b = 95; c = +3;
Δ = b2-4ac
Δ = 952-4·(-10)·3
Δ = 9145
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{-(95)-\sqrt{9145}}{2*-10}=\frac{-95-\sqrt{9145}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(95)+\sqrt{9145}}{2*-10}=\frac{-95+\sqrt{9145}}{-20}
$