(1/5x)+3=4x-35

Solution for (1/5x)+3=4x-35 equation:

(1/5x)+3=4x-35

We move all terms to the left:

(1/5x)+3-(4x-35)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/5x)-(4x-35)+3=0

We get rid of parentheses

1/5x-4x+35+3=0

We multiply all the terms by the denominator


-4x*5x+35*5x+3*5x+1=0

Wy multiply elements

-20x^2+175x+15x+1=0

We add all the numbers together, and all the variables

-20x^2+190x+1=0

a = -20; b = 190; c = +1;
Δ = b2-4ac
Δ = 1902-4·(-20)·1
Δ = 36180
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:

$\sqrt{\Delta}=\sqrt{36180}=\sqrt{36*1005}=\sqrt{36}*\sqrt{1005}=6\sqrt{1005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-6\sqrt{1005}}{2*-20}=\frac{-190-6\sqrt{1005}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+6\sqrt{1005}}{2*-20}=\frac{-190+6\sqrt{1005}}{-40}
$