1/5x-30=x-6

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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} $

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