1/5x-30=x-6

Solution for 1/5x-30=x-6 equation:

1/5x-30=x-6

We move all terms to the left:

1/5x-30-(x-6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x+6-30=0

We multiply all the terms by the denominator


-x*5x+6*5x-30*5x+1=0

Wy multiply elements

-5x^2+30x-150x+1=0

We add all the numbers together, and all the variables

-5x^2-120x+1=0

a = -5; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·(-5)·1
Δ = 14420
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:

$\sqrt{\Delta}=\sqrt{14420}=\sqrt{4*3605}=\sqrt{4}*\sqrt{3605}=2\sqrt{3605}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3605}}{2*-5}=\frac{120-2\sqrt{3605}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3605}}{2*-5}=\frac{120+2\sqrt{3605}}{-10}
$