1/3x-5=2x-35

Solution for 1/3x-5=2x-35 equation:

1/3x-5=2x-35

We move all terms to the left:

1/3x-5-(2x-35)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x+35-5=0

We multiply all the terms by the denominator


-2x*3x+35*3x-5*3x+1=0

Wy multiply elements

-6x^2+105x-15x+1=0

We add all the numbers together, and all the variables

-6x^2+90x+1=0

a = -6; b = 90; c = +1;
Δ = b2-4ac
Δ = 902-4·(-6)·1
Δ = 8124
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:

$\sqrt{\Delta}=\sqrt{8124}=\sqrt{4*2031}=\sqrt{4}*\sqrt{2031}=2\sqrt{2031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2031}}{2*-6}=\frac{-90-2\sqrt{2031}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2031}}{2*-6}=\frac{-90+2\sqrt{2031}}{-12}
$